78:@0.067867:0.963104:0.095634:0.963104:0.095634:0.941283:0.067867:0.941283:0.000000:0.000000
Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
10.º EGB:@0.120102:0.967458:0.179272:0.967458:0.179272:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DUA:@0.070720:0.123711:0.114363:0.123711:0.114363:0.103460:0.070720:0.103460:0.000000:0.000000:0.000000
. Representación:@0.114363:0.123082:0.246653:0.123082:0.246653:0.106182:0.114363:0.106182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Método de reducción :@0.287490:0.150300:0.460966:0.150300:0.460966:0.133400:0.287490:0.133400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Antes de resolver un sistema de ecuaciones lineales conviene analizar los coeficientes :@0.287490:0.174019:0.907597:0.174019:0.907597:0.157630:0.287490:0.157630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de ambas ecuaciones, para seleccionar el método que más convenga. Los métodos :@0.287490:0.190616:0.907648:0.190616:0.907648:0.174227:0.287490:0.174227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de suma y resta, llamados también de reducción, y el método de sustitución son de :@0.287490:0.207212:0.907599:0.207212:0.907599:0.190823:0.287490:0.190823:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mucha ayuda en la solución de un sistema de ecuaciones lineales con dos incógnitas, :@0.287490:0.223808:0.907597:0.223808:0.907597:0.207419:0.287490:0.207419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
debido a su simplicidad. Analicemos un ejemplo. :@0.287490:0.240405:0.649846:0.240405:0.649846:0.224016:0.287490:0.224016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un restaurante de comida vegetariana vende combos de hamburguesas y pizzas. En :@0.287490:0.264124:0.907726:0.264124:0.907726:0.247735:0.287490:0.247735:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cierto día, reportan una venta de 600 dólares. Si el combo de hamburguesa cuesta :@0.287490:0.280720:0.907597:0.280720:0.907597:0.264331:0.287490:0.264331:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 dólares y el de pizza cuesta 6 dólares y en total han vendido 110 combos, ¿cuántos :@0.287490:0.297316:0.907634:0.297316:0.907634:0.280928:0.287490:0.280928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de cada uno vendieron?:@0.287490:0.313913:0.464762:0.313913:0.464762:0.297524:0.287490:0.297524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución. :@0.287490:0.337632:0.358510:0.337632:0.358510:0.320994:0.287490:0.320994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Identificamos y simbolizamos las variables::@0.358510:0.337632:0.669895:0.337632:0.669895:0.321243:0.358510:0.321243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.287490:0.361351:0.294953:0.361351:0.294953:0.345958:0.287490:0.345958:0.000000
: cantidad de combos de hamburguesas:@0.294953:0.361351:0.590068:0.361351:0.590068:0.344962:0.294953:0.344962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.287490:0.385070:0.294972:0.385070:0.294972:0.369677:0.287490:0.369677:0.000000
: cantidad de combos de pizzas:@0.294972:0.385070:0.524783:0.385070:0.524783:0.368681:0.294972:0.368681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De acuerdo con la información proporcionada, elaboramos el siguiente cuadro y :@0.287490:0.408789:0.907599:0.408789:0.907599:0.392400:0.287490:0.392400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
planteamos el sistema de ecuaciones::@0.287490:0.425385:0.564067:0.425385:0.564067:0.408996:0.287490:0.408996:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
N.º de combos:@0.544532:0.450595:0.646603:0.450595:0.646603:0.435042:0.544532:0.435042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Valor de la venta:@0.677681:0.450595:0.798380:0.450595:0.798380:0.435042:0.677681:0.435042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Hamburguesa:@0.405705:0.471982:0.500507:0.471982:0.500507:0.457083:0.405705:0.457083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.592176:0.471982:0.598961:0.471982:0.598961:0.457988:0.592176:0.457988:0.000000
5x:@0.730350:0.471982:0.745712:0.471982:0.745712:0.457083:0.730350:0.457083:0.000000:0.000000
Pizza:@0.436781:0.493369:0.469448:0.493369:0.469448:0.478470:0.436781:0.478470:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.592176:0.493369:0.598978:0.493369:0.598978:0.479375:0.592176:0.479375:0.000000
6y:@0.730266:0.493369:0.745813:0.493369:0.745813:0.478470:0.730266:0.478470:0.000000:0.000000
Total:@0.437150:0.514755:0.469080:0.514755:0.469080:0.499856:0.437150:0.499856:0.000000:0.000000:0.000000:0.000000:0.000000
110:@0.583314:0.514755:0.607840:0.514755:0.607840:0.499856:0.583314:0.499856:0.000000:0.000000:0.000000
600:@0.725777:0.514755:0.750302:0.514755:0.750302:0.499856:0.725777:0.499856:0.000000:0.000000:0.000000
Ecuación:@0.422826:0.536142:0.483403:0.536142:0.483403:0.521243:0.422826:0.521243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.559191:0.536142:0.565976:0.536142:0.565976:0.522148:0.559191:0.522148:0.000000
 +   = 110 :@0.565976:0.536142:0.635615:0.536142:0.635615:0.521243:0.565976:0.521243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.583298:0.536142:0.590099:0.536142:0.590099:0.522148:0.583298:0.522148:0.000000
5  + 6  = 600:@0.693478:0.536142:0.782584:0.536142:0.782584:0.521243:0.693478:0.521243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.701653:0.536142:0.708438:0.536142:0.708438:0.522148:0.701653:0.522148:0.000000
y:@0.733935:0.536142:0.740737:0.536142:0.740737:0.522148:0.733935:0.522148:0.000000
Resolvamos el sistema de ecuaciones mediante el método de reducción o de suma :@0.287495:0.566335:0.907676:0.566335:0.907676:0.549946:0.287495:0.549946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y resta, que consiste en eliminar una de las incógnitas, mediante una suma algebraica :@0.287495:0.582931:0.907582:0.582931:0.907582:0.566542:0.287495:0.566542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de ecuaciones; para ello, los coeficientes deben ser iguales en valor y distintos en :@0.287495:0.599528:0.907731:0.599528:0.907731:0.583139:0.287495:0.583139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
signo, con lo que se obtiene una nueva ecuación con una sola variable. Después de :@0.287495:0.616124:0.907659:0.616124:0.907659:0.599735:0.287495:0.599735:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resolver esa ecuación, se reemplaza el valor en una de las ecuaciones originales, para :@0.287495:0.632720:0.907659:0.632720:0.907659:0.616331:0.287495:0.616331:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
determinar la otra incógnita.:@0.287495:0.649317:0.495466:0.649317:0.495466:0.632928:0.287495:0.632928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Así, tenemos: :@0.287495:0.681362:0.388442:0.681362:0.388442:0.664973:0.287495:0.664973:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.666152:0.671046:0.673614:0.671046:0.673614:0.655654:0.666152:0.655654:0.000000
y:@0.692648:0.671046:0.700130:0.671046:0.700130:0.655654:0.692648:0.655654:0.000000
x:@0.674204:0.691790:0.681666:0.691790:0.681666:0.676398:0.674204:0.676398:0.000000
y:@0.709914:0.691790:0.717395:0.691790:0.717395:0.676398:0.709914:0.676398:0.000000
+=:@0.677957:0.670632:0.715141:0.670632:0.715141:0.653691:0.677957:0.653691:0.000000:0.000000
+:@0.686018:0.691376:0.696134:0.691376:0.696134:0.674435:0.686018:0.674435:0.000000
=:@0.722300:0.691376:0.732416:0.691376:0.732416:0.674435:0.722300:0.674435:0.000000
:@0.655688:0.671932:0.664791:0.671932:0.664791:0.654991:0.655688:0.654991:0.000000
:@0.655688:0.683382:0.664791:0.683382:0.664791:0.666442:0.655688:0.666442:0.000000
:@0.655688:0.694833:0.664791:0.694833:0.664791:0.677892:0.655688:0.677892:0.000000
110:@0.717112:0.671046:0.743941:0.671046:0.743941:0.654659:0.717112:0.654659:0.000000:0.000000:0.000000
5:@0.664712:0.691791:0.673705:0.691791:0.673705:0.675403:0.664712:0.675403:0.000000
6:@0.699262:0.691791:0.708254:0.691791:0.708254:0.675403:0.699262:0.675403:0.000000
600:@0.735820:0.691791:0.762648:0.691791:0.762648:0.675403:0.735820:0.675403:0.000000:0.000000:0.000000
Multiplicamos a la primera ecuación por –5, :@0.287495:0.725703:0.626546:0.725703:0.626546:0.709314:0.287495:0.709314:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con lo que se obtiene el sistema equivalente::@0.287495:0.742299:0.617271:0.742299:0.617271:0.725910:0.287495:0.725910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.665289:0.721486:0.675405:0.721486:0.675405:0.704545:0.665289:0.704545:0.000000
−:@0.696669:0.721486:0.706785:0.721486:0.706785:0.704545:0.696669:0.704545:0.000000
=−:@0.731513:0.721486:0.755449:0.721486:0.755449:0.704545:0.731513:0.704545:0.000000:0.000000
+:@0.686018:0.742230:0.696134:0.742230:0.696134:0.725289:0.686018:0.725289:0.000000
=:@0.722300:0.742230:0.732416:0.742230:0.732416:0.725289:0.722300:0.725289:0.000000
:@0.655688:0.722786:0.664791:0.722786:0.664791:0.705845:0.655688:0.705845:0.000000
:@0.655688:0.734236:0.664791:0.734236:0.664791:0.717296:0.655688:0.717296:0.000000
:@0.655691:0.745686:0.664794:0.745686:0.664794:0.728745:0.655691:0.728745:0.000000
5:@0.675365:0.721900:0.684357:0.721900:0.684357:0.705513:0.675365:0.705513:0.000000
5:@0.709343:0.721900:0.718335:0.721900:0.718335:0.705513:0.709343:0.705513:0.000000
550:@0.755409:0.721900:0.782238:0.721900:0.782238:0.705513:0.755409:0.705513:0.000000:0.000000:0.000000
5:@0.664715:0.742644:0.673707:0.742644:0.673707:0.726257:0.664715:0.726257:0.000000
6:@0.699264:0.742644:0.708256:0.742644:0.708256:0.726257:0.699264:0.726257:0.000000
600:@0.735822:0.742644:0.762651:0.742644:0.762651:0.726257:0.735822:0.726257:0.000000:0.000000:0.000000
x:@0.684855:0.721900:0.692318:0.721900:0.692318:0.706508:0.684855:0.706508:0.000000
y:@0.719109:0.721900:0.726590:0.721900:0.726590:0.706508:0.719109:0.706508:0.000000
x:@0.674205:0.742644:0.681667:0.742644:0.681667:0.727252:0.674205:0.727252:0.000000
y:@0.709915:0.742644:0.717396:0.742644:0.717396:0.727252:0.709915:0.727252:0.000000
Ahora, sumamos las dos ecuaciones para :@0.287495:0.787717:0.626490:0.787717:0.626490:0.771328:0.287495:0.771328:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
eliminar una de las incógnitas.:@0.287495:0.804313:0.508384:0.804313:0.508384:0.787924:0.287495:0.787924:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.655691:0.772117:0.665807:0.772117:0.665807:0.755176:0.655691:0.755176:0.000000
−:@0.687071:0.772117:0.697187:0.772117:0.697187:0.755176:0.687071:0.755176:0.000000
=−:@0.721915:0.772117:0.745851:0.772117:0.745851:0.755176:0.721915:0.755176:0.000000:0.000000
+:@0.685921:0.792861:0.696037:0.792861:0.696037:0.775920:0.685921:0.775920:0.000000
=:@0.722202:0.792861:0.732318:0.792861:0.732318:0.775920:0.722202:0.775920:0.000000
=:@0.720765:0.816191:0.730881:0.816191:0.730881:0.799251:0.720765:0.799251:0.000000
5:@0.665768:0.772532:0.674760:0.772532:0.674760:0.756144:0.665768:0.756144:0.000000
5:@0.699746:0.772532:0.708738:0.772532:0.708738:0.756144:0.699746:0.756144:0.000000
550:@0.745812:0.772532:0.772640:0.772532:0.772640:0.756144:0.745812:0.756144:0.000000:0.000000:0.000000
5   :@0.664617:0.793276:0.664046:0.793262:0.664046:0.776875:0.664617:0.776888:0.000000:0.000000:0.000000:0.000000
6:@0.699166:0.793276:0.708158:0.793276:0.708158:0.776888:0.699166:0.776888:0.000000
600:@0.745232:0.793276:0.772061:0.793276:0.772061:0.776888:0.745232:0.776888:0.000000:0.000000:0.000000
50:@0.743500:0.816606:0.761410:0.816606:0.761410:0.800219:0.743500:0.800219:0.000000:0.000000
x:@0.675267:0.772518:0.682730:0.772518:0.682730:0.757126:0.675267:0.757126:0.000000
y:@0.709522:0.772518:0.717003:0.772518:0.717003:0.757126:0.709522:0.757126:0.000000
x:@0.674125:0.793262:0.681588:0.793262:0.681588:0.777870:0.674125:0.777870:0.000000
y:@0.709835:0.793262:0.717316:0.793262:0.717316:0.777870:0.709835:0.777870:0.000000
y:@0.708379:0.816592:0.715861:0.816592:0.715861:0.801200:0.708379:0.801200:0.000000
  :@0.736295:0.793262:0.744366:0.793262:0.744366:0.776875:0.736295:0.776875:0.000000:0.000000
             :@0.655975:0.816592:0.708435:0.816592:0.708435:0.800205:0.655975:0.800205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.734858:0.816592:0.742929:0.816592:0.742929:0.800205:0.734858:0.800205:0.000000:0.000000
Finalmente, reemplazamos el valor obtenido en cualquiera de las ecuaciones :@0.287495:0.838636:0.907713:0.838636:0.907713:0.822247:0.287495:0.822247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
iniciales, para hallar el valor de la otra incógnita::@0.287495:0.855232:0.634556:0.855232:0.634556:0.838844:0.287495:0.838844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.507872:0.878951:0.515335:0.878951:0.515335:0.863558:0.507872:0.863558:0.000000
 + 50 = 110            = 60:@0.515335:0.878951:0.683266:0.878951:0.683266:0.862563:0.515335:0.862563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.638763:0.878951:0.646226:0.878951:0.646226:0.863558:0.638763:0.863558:0.000000
La solución para el problema planteado es: vendieron 60 combos de hamburguesas :@0.287495:0.902670:0.907676:0.902670:0.907676:0.886282:0.287495:0.886282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y 50 combos de pizzas.:@0.287495:0.919267:0.455775:0.919267:0.455775:0.902878:0.287495:0.902878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sistemas de ecuaciones lineales: :@0.286308:0.063945:0.853530:0.063945:0.853530:0.027071:0.286308:0.027071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
método de reducción y de sustitución:@0.286308:0.094120:0.939088:0.094120:0.939088:0.057246:0.286308:0.057246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.094760:0.108604:0.159692:0.108604:0.159692:0.011516:0.094760:0.011516:0.000000
©:@0.070380:0.277495:0.070380:0.272388:0.058298:0.272388:0.058298:0.277495:0.000000
Shutterstock:@0.070380:0.272388:0.070380:0.234670:0.058469:0.234670:0.058469:0.272388:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En los negocios se :@0.122826:0.394032:0.248637:0.394032:0.248637:0.379133:0.122826:0.379133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pueden aplicar los :@0.122508:0.409119:0.248637:0.409119:0.248637:0.394220:0.122508:0.394220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sistemas de ecuaciones, :@0.085552:0.424207:0.248633:0.424207:0.248633:0.409308:0.085552:0.409308:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por ejemplo, en poner :@0.095670:0.439295:0.248635:0.439295:0.248635:0.424396:0.095670:0.424396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
precio a las mercancías.:@0.088718:0.454382:0.244966:0.454382:0.244966:0.439483:0.088718:0.439483:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Educación :@0.142621:0.159772:0.224305:0.159772:0.224305:0.142871:0.142621:0.142871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
financiera:@0.145807:0.173602:0.220856:0.173602:0.220856:0.156701:0.145807:0.156701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.150700:0.173602:0.154324:0.173602:0.154324:0.156701:0.150700:0.156701:0.000000
Ecuaciones equivalentes:@0.071615:0.603722:0.244967:0.603722:0.244967:0.588358:0.071615:0.588358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las ecuaciones :@0.144605:0.622368:0.248637:0.622368:0.248637:0.607469:0.144605:0.607469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
equivalentes son las que :@0.081432:0.637455:0.248636:0.637455:0.248636:0.622556:0.081432:0.622556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tienen la misma solución :@0.078651:0.652543:0.248637:0.652543:0.248637:0.637644:0.078651:0.637644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y son útiles para :@0.137552:0.667631:0.248637:0.667631:0.248637:0.652732:0.137552:0.652732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
simplificar y resolver :@0.110463:0.682718:0.248636:0.682718:0.248636:0.667819:0.110463:0.667819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sistemas de ecuaciones y :@0.077243:0.697806:0.248637:0.697806:0.248637:0.682907:0.077243:0.682907:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
otros problemas :@0.135877:0.712893:0.248637:0.712893:0.248637:0.697994:0.135877:0.697994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemáticos.:@0.155075:0.727981:0.244967:0.727981:0.244967:0.713082:0.155075:0.713082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A partir de una ecuación :@0.080962:0.746627:0.248636:0.746627:0.248636:0.731728:0.080962:0.731728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dada, se pueden obtener :@0.077344:0.761714:0.248634:0.761714:0.248634:0.746815:0.077344:0.746815:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuaciones equivalentes, :@0.078349:0.776802:0.248634:0.776802:0.248634:0.761903:0.078349:0.761903:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
multiplicando o :@0.139160:0.791890:0.248637:0.791890:0.248637:0.776991:0.139160:0.776991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dividiendo cada término :@0.081030:0.806977:0.248636:0.806977:0.248636:0.792078:0.081030:0.792078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la ecuación por un :@0.099960:0.822065:0.248637:0.822065:0.248637:0.807166:0.099960:0.807166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mismo número real, :@0.111368:0.837152:0.248636:0.837152:0.248636:0.822253:0.111368:0.822253:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
excepto cero.:@0.155460:0.852240:0.244967:0.852240:0.244967:0.837341:0.155460:0.837341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Obtén dos ecuaciones :@0.105052:0.870886:0.247984:0.870886:0.247984:0.856892:0.105052:0.856892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
equivalentes a la ecuación :@0.077595:0.885973:0.247984:0.885973:0.247984:0.871980:0.077595:0.871980:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2x – y = 5 :@0.185481:0.904619:0.247984:0.904619:0.247984:0.890626:0.185481:0.890626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
     Matemática:@0.116009:0.571281:0.223549:0.571281:0.223549:0.554380:0.116009:0.554380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000