66:@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
Una ecuación lineal con dos incógnitas es una ecuación algebraica que contiene :@0.287490:0.150300:0.907671:0.150300:0.907671:0.133911:0.287490:0.133911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dos variables o incógnitas que son de primer grado; es decir, son funciones lineales. :@0.287490:0.166897:0.907578:0.166897:0.907578:0.150508:0.287490:0.150508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Su resolución implica encontrar los valores de las incógnitas que son pares :@0.287490:0.183493:0.907672:0.183493:0.907672:0.167104:0.287490:0.167104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ordenados y que satisfacen la igualdad.:@0.287490:0.200089:0.574937:0.200089:0.574937:0.183700:0.287490:0.183700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las ecuaciones lineales con dos incógnitas tienen una amplia gama de aplicaciones en :@0.287490:0.223808:0.907617:0.223808:0.907617:0.207419:0.287490:0.207419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diversos campos: geometría analítica, física, economía, biología, entre otras ciencias.:@0.287490:0.240405:0.884914:0.240405:0.884914:0.224016:0.287490:0.224016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición de ecuación lineal:@0.296992:0.268772:0.539003:0.268772:0.539003:0.251871:0.296992:0.251871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Es una expresión de la forma :@0.539003:0.268772:0.788347:0.268772:0.788347:0.252383:0.539003:0.252383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax:@0.793046:0.268772:0.809778:0.268772:0.809778:0.253379:0.793046:0.253379:0.000000:0.000000
 + :@0.809778:0.268772:0.833531:0.268772:0.833531:0.252383:0.809778:0.252383:0.000000:0.000000:0.000000
by:@0.838230:0.268772:0.854871:0.268772:0.854871:0.253379:0.838230:0.253379:0.000000:0.000000
 =  , :@0.854834:0.268772:0.898194:0.268772:0.898194:0.252383:0.854834:0.252383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.883286:0.268772:0.890952:0.268772:0.890952:0.253379:0.883286:0.253379:0.000000
donde  ,   y   son números reales y el grado de las incógnitas  y   es 1.:@0.296992:0.285368:0.826063:0.285368:0.826063:0.268979:0.296992:0.268979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.349695:0.285368:0.399321:0.285368:0.399321:0.269975:0.349695:0.269975:0.000000:0.000000:0.000000:0.000000:0.000000
x    y:@0.752942:0.285368:0.789981:0.285368:0.789981:0.269975:0.752942:0.269975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo. :@0.287502:0.317192:0.354006:0.317192:0.354006:0.300554:0.287502:0.300554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para la nota de su parcial, Fabián rindió dos exámenes de matemática. Si su profesora :@0.287502:0.340911:0.907692:0.340911:0.907692:0.324522:0.287502:0.324522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
le dice que la suma de sus calificaciones es 14, ¿qué calificación obtuvo Fabián en :@0.287502:0.357507:0.907666:0.357507:0.907666:0.341118:0.287502:0.341118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cada examen?:@0.287502:0.374104:0.392650:0.374104:0.392650:0.357715:0.287502:0.357715:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución. :@0.287502:0.397823:0.358522:0.397823:0.358522:0.381185:0.287502:0.381185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los datos que desconocemos son las variables, siendo   el primer examen y   el :@0.287502:0.421542:0.907627:0.421542:0.907627:0.405153:0.287502:0.405153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.707982:0.421542:0.715445:0.421542:0.715445:0.406148:0.707982:0.406148:0.000000
y:@0.876816:0.421542:0.884298:0.421542:0.884298:0.406148:0.876816:0.406148:0.000000
segundo examen. La ecuación planteada es:   +   = 14:@0.287502:0.438138:0.686696:0.438138:0.686696:0.421749:0.287502:0.421749:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.615658:0.438138:0.623121:0.438138:0.623121:0.422745:0.615658:0.422745:0.000000
y:@0.642175:0.438138:0.649657:0.438138:0.649657:0.422745:0.642175:0.422745:0.000000
A continuación, resolveremos la ecuación planteada anteriormente.:@0.287502:0.461857:0.782682:0.461857:0.782682:0.445468:0.287502:0.445468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Primero:@0.287502:0.485576:0.350783:0.485576:0.350783:0.468675:0.287502:0.468675:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: despejamos la variable  .  :@0.350783:0.485576:0.547457:0.485576:0.547457:0.469187:0.350783:0.469187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.528698:0.485576:0.536179:0.485576:0.536179:0.470183:0.528698:0.470183:0.000000
→  :@0.547457:0.485161:0.574859:0.485161:0.574859:0.468219:0.547457:0.468219:0.000000:0.000000:0.000000
y:@0.574859:0.485576:0.582341:0.485576:0.582341:0.470183:0.574859:0.470183:0.000000
 = 14 – :@0.582341:0.485576:0.636665:0.485576:0.636665:0.469187:0.582341:0.469187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.636665:0.485576:0.644128:0.485576:0.644128:0.470183:0.636665:0.470183:0.000000
Segundo:@0.287502:0.509295:0.359370:0.509295:0.359370:0.492394:0.287502:0.492394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: asignamos valores positivos arbitrarios a  , efectuamos las operaciones y :@0.359370:0.509295:0.907708:0.509295:0.907708:0.492906:0.359370:0.492906:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.669430:0.509295:0.676893:0.509295:0.676893:0.493902:0.669430:0.493902:0.000000
obtenemos los valores de  . Organizamos los datos en una tabla de valores.:@0.287502:0.525891:0.838006:0.525891:0.838006:0.509502:0.287502:0.509502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.479719:0.525891:0.487201:0.525891:0.487201:0.510498:0.479719:0.510498:0.000000
Como se puede observar, estas son algunas soluciones para el problema planteado.:@0.287502:0.549610:0.900144:0.549610:0.900144:0.533221:0.287502:0.533221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.474695:0.573870:0.483038:0.573870:0.483038:0.558317:0.474695:0.558317:0.000000
y:@0.564153:0.573870:0.572479:0.573870:0.572479:0.558317:0.564153:0.558317:0.000000
 = 14 – :@0.572479:0.573870:0.622669:0.573870:0.622669:0.558506:0.572479:0.558506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.622669:0.573870:0.631012:0.573870:0.631012:0.558317:0.622669:0.558317:0.000000
y:@0.712144:0.573870:0.720470:0.573870:0.720470:0.558317:0.712144:0.558317:0.000000
Si   = 4:@0.455262:0.593672:0.502487:0.593672:0.502487:0.578773:0.455262:0.578773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.470205:0.593672:0.476990:0.593672:0.476990:0.579679:0.470205:0.579679:0.000000
y:@0.565409:0.593672:0.572211:0.593672:0.572211:0.579679:0.565409:0.579679:0.000000
 = 14 – 4:@0.572211:0.593672:0.629772:0.593672:0.629772:0.578773:0.572211:0.578773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.696078:0.593672:0.702879:0.593672:0.702879:0.579679:0.696078:0.579679:0.000000
 = 10:@0.702879:0.593672:0.736552:0.593672:0.736552:0.578773:0.702879:0.578773:0.000000:0.000000:0.000000:0.000000:0.000000
Si   = 5:@0.455262:0.613161:0.502487:0.613161:0.502487:0.598262:0.455262:0.598262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.470205:0.613161:0.476990:0.613161:0.476990:0.599167:0.470205:0.599167:0.000000
y :@0.565744:0.613161:0.575561:0.613161:0.575561:0.599167:0.565744:0.599167:0.000000:0.000000
= 14 – 5:@0.575561:0.613161:0.629454:0.613161:0.629454:0.598262:0.575561:0.598262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.700166:0.613161:0.706967:0.613161:0.706967:0.599167:0.700166:0.599167:0.000000
 = 9:@0.706967:0.613161:0.732464:0.613161:0.732464:0.598262:0.706967:0.598262:0.000000:0.000000:0.000000:0.000000
Si   = 7:@0.455262:0.632649:0.502487:0.632649:0.502487:0.617750:0.455262:0.617750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.470205:0.632649:0.476990:0.632649:0.476990:0.618655:0.470205:0.618655:0.000000
y :@0.565744:0.632649:0.575561:0.632649:0.575561:0.618655:0.565744:0.618655:0.000000:0.000000
= 14 – 7:@0.575561:0.632649:0.629454:0.632649:0.629454:0.617750:0.575561:0.617750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.700166:0.632649:0.706967:0.632649:0.706967:0.618655:0.700166:0.618655:0.000000
 = 7:@0.706967:0.632649:0.732464:0.632649:0.732464:0.617750:0.706967:0.617750:0.000000:0.000000:0.000000:0.000000
a) :@0.287494:0.661904:0.306216:0.661904:0.306216:0.645003:0.287494:0.645003:0.000000:0.000000:0.000000
Si en el primer examen obtuvo 4, en el segundo sacó 10.:@0.311229:0.661904:0.724946:0.661904:0.724946:0.645515:0.311229:0.645515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b) :@0.287494:0.685623:0.307525:0.685623:0.307525:0.668722:0.287494:0.668722:0.000000:0.000000:0.000000
Si en el primer examen obtuvo 5, en el segundo sacó 9.:@0.311229:0.685623:0.715953:0.685623:0.715953:0.669234:0.311229:0.669234:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c) :@0.287494:0.709342:0.305129:0.709342:0.305129:0.692441:0.287494:0.692441:0.000000:0.000000:0.000000
Si en el primer examen obtuvo 7, en el segundo sacó 7.:@0.311229:0.709342:0.715953:0.709342:0.715953:0.692953:0.311229:0.692953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Podemos concluir que para todo valor de  , existe uno para  . Por lo tanto, no hay :@0.287494:0.733061:0.907600:0.733061:0.907600:0.716672:0.287494:0.716672:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.604375:0.733061:0.611839:0.733061:0.611839:0.717667:0.604375:0.717667:0.000000
y:@0.740314:0.733061:0.747796:0.733061:0.747796:0.717667:0.740314:0.717667:0.000000
solución única para el problema.:@0.287494:0.749657:0.525927:0.749657:0.525927:0.733268:0.287494:0.733268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.382043:0.873053:0.386660:0.873053:0.386660:0.864638:0.382043:0.864638:0.000000
0:@0.363592:0.870923:0.368209:0.870923:0.368209:0.862508:0.363592:0.862508:0.000000
0:@0.355890:0.863999:0.360507:0.863999:0.360507:0.855584:0.355890:0.855584:0.000000
4:@0.404165:0.873053:0.408782:0.873053:0.408782:0.864638:0.404165:0.864638:0.000000
6:@0.426287:0.873053:0.430904:0.873053:0.430904:0.864638:0.426287:0.864638:0.000000
8:@0.448484:0.873053:0.453102:0.873053:0.453102:0.864638:0.448484:0.864638:0.000000
10:@0.468515:0.873053:0.477750:0.873053:0.477750:0.864638:0.468515:0.864638:0.000000:0.000000
12:@0.490590:0.873053:0.499825:0.873053:0.499825:0.864638:0.490590:0.864638:0.000000:0.000000
14:@0.512750:0.873053:0.521984:0.873053:0.521984:0.864638:0.512750:0.864638:0.000000:0.000000
16:@0.534824:0.873053:0.544059:0.873053:0.544059:0.864638:0.534824:0.864638:0.000000:0.000000
-2:@0.336386:0.873053:0.343823:0.873053:0.343823:0.864638:0.336386:0.864638:0.000000:0.000000
2:@0.353662:0.854103:0.358280:0.854103:0.358280:0.845688:0.353662:0.845688:0.000000
4:@0.353662:0.840369:0.358280:0.840369:0.358280:0.831954:0.353662:0.831954:0.000000
6:@0.353662:0.827211:0.358280:0.827211:0.358280:0.818796:0.353662:0.818796:0.000000
8:@0.353662:0.813697:0.358280:0.813697:0.358280:0.805282:0.353662:0.805282:0.000000
10:@0.349319:0.800147:0.358554:0.800147:0.358554:0.791732:0.349319:0.791732:0.000000:0.000000
12:@0.349322:0.786874:0.358557:0.786874:0.358557:0.778459:0.349322:0.778459:0.000000:0.000000
14:@0.349275:0.773325:0.358509:0.773325:0.358509:0.764910:0.349275:0.764910:0.000000:0.000000
y:@0.353502:0.762754:0.357665:0.762754:0.357665:0.754339:0.353502:0.754339:0.000000
x:@0.555695:0.873131:0.559754:0.873131:0.559754:0.864716:0.555695:0.864716:0.000000
A:@0.409309:0.797691:0.417416:0.797691:0.417416:0.786446:0.409309:0.786446:0.000000
B:@0.420476:0.804481:0.427655:0.804481:0.427655:0.793237:0.420476:0.793237:0.000000
C:@0.442531:0.818360:0.450214:0.818360:0.450214:0.807115:0.442531:0.807115:0.000000
x:@0.655028:0.794399:0.663371:0.794399:0.663371:0.778846:0.655028:0.778846:0.000000
y:@0.740515:0.794399:0.748841:0.794399:0.748841:0.778846:0.740515:0.778846:0.000000
Puntos:@0.804945:0.794399:0.855353:0.794399:0.855353:0.779035:0.804945:0.779035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.655112:0.815421:0.663287:0.815421:0.663287:0.800522:0.655112:0.800522:0.000000
10:@0.736495:0.815421:0.752845:0.815421:0.752845:0.800522:0.736495:0.800522:0.000000:0.000000
A (4, 10):@0.803421:0.815421:0.856878:0.815421:0.856878:0.800522:0.803421:0.800522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.655112:0.834909:0.663287:0.834909:0.663287:0.820010:0.655112:0.820010:0.000000
9:@0.740582:0.834909:0.748758:0.834909:0.748758:0.820010:0.740582:0.820010:0.000000
B (5, 9):@0.808178:0.834909:0.852120:0.834909:0.852120:0.820010:0.808178:0.820010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
7:@0.655112:0.854398:0.663287:0.854398:0.663287:0.839499:0.655112:0.839499:0.000000
7:@0.740582:0.854398:0.748758:0.854398:0.748758:0.839499:0.740582:0.839499:0.000000
C (7, 7):@0.807626:0.854398:0.852656:0.854398:0.852656:0.839499:0.807626:0.839499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Como se puede observar, la solución es una línea recta, donde cada par ordenado :@0.287494:0.904158:0.907680:0.904158:0.907680:0.887769:0.287494:0.887769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ) de la recta satisface la ecuación.:@0.287494:0.920754:0.556093:0.920754:0.556093:0.904365:0.287494:0.904365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.292377:0.920754:0.314564:0.920754:0.314564:0.905361:0.292377:0.905361:0.000000:0.000000:0.000000
Ecuaciones lineales con :@0.286308:0.063945:0.701231:0.063945:0.701231:0.027071:0.286308:0.027071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dos incógnitas:@0.286308:0.094120:0.539081:0.094120:0.539081:0.057246:0.286308:0.057246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.094760:0.108604:0.159692:0.108604:0.159692:0.011516:0.094760:0.011516:0.000000
Las ecuaciones lineales :@0.091039:0.292956:0.248428:0.292956:0.248428:0.278057:0.091039:0.278057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tienen gran aplicación :@0.096182:0.308044:0.248426:0.308044:0.248426:0.293145:0.096182:0.293145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en los negocios. :@0.137611:0.323131:0.248426:0.323131:0.248426:0.308232:0.137611:0.308232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Tienes en mente algún :@0.096216:0.341777:0.247775:0.341777:0.247775:0.327783:0.096216:0.327783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
emprendimiento tuyo?:@0.100588:0.356865:0.244758:0.356865:0.244758:0.342871:0.100588:0.342871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Educación :@0.142411:0.159772:0.224095:0.159772:0.224095:0.142871:0.142411:0.142871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
financiera:@0.145597:0.173602:0.220647:0.173602:0.220647:0.156701:0.145597:0.156701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.150490:0.173602:0.154114:0.173602:0.154114:0.156701:0.150490:0.156701:0.000000
©:@0.066399:0.253669:0.066399:0.248562:0.054317:0.248562:0.054317:0.253669:0.000000
Shutterstock:@0.066399:0.248562:0.066399:0.210844:0.054488:0.210844:0.054488:0.248562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Con el objetivo de :@0.122583:0.495340:0.248425:0.495340:0.248425:0.480441:0.122583:0.480441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
construir una tabla de :@0.098778:0.510428:0.248427:0.510428:0.248427:0.495529:0.098778:0.495529:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
valores, se asignan valores :@0.071204:0.525515:0.248425:0.525515:0.248425:0.510616:0.071204:0.510616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
arbitrarios a la variable :@0.095846:0.540603:0.248425:0.540603:0.248425:0.525704:0.095846:0.525704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
independiente   para :@0.099214:0.555691:0.248425:0.555691:0.248425:0.540792:0.099214:0.540792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x,:@0.201871:0.555691:0.211687:0.555691:0.211687:0.541697:0.201871:0.541697:0.000000:0.000000
reemplazar en la ecuación :@0.070098:0.570778:0.248427:0.570778:0.248427:0.555879:0.070098:0.555879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y obtener el valor de la :@0.092982:0.585866:0.248427:0.585866:0.248427:0.570967:0.092982:0.570967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
variable dependiente  .:@0.088928:0.600953:0.244755:0.600953:0.244755:0.586054:0.088928:0.586054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.235039:0.600953:0.241840:0.600953:0.241840:0.586960:0.235039:0.586960:0.000000
¿Qué es una tabla de :@0.112749:0.619599:0.247774:0.619599:0.247774:0.605605:0.112749:0.605605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
valores?:@0.194267:0.634687:0.244758:0.634687:0.244758:0.620693:0.194267:0.620693:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
     Matemática:@0.115799:0.462899:0.223340:0.462899:0.223340:0.445999:0.115799:0.445999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.53. :@0.290067:0.965521:0.338404:0.965521:0.338404:0.954766:0.290067:0.954766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reconocer la recta como la solución gráfica de una ecuación lineal con dos incógnitas en R.:@0.338404:0.965521:0.764571:0.965521:0.764571:0.955091:0.338404:0.955091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.527542:0.965521:0.530110:0.965521:0.530110:0.955091:0.527542:0.955091:0.000000