Question

Resuelve Por Cualquiera De Los 3 métodos para saber la solucion

2×+y=6
2×-y=2
×-y=6
×+y=14
5×+y=8
4×+y=6

Answer 1

$\left \{ {{2x+y=6} \atop {2x-y=2}} \right.$

$\left \{ {{2x = 6-y} \atop {2x = 2+y}} \right.$

$\left \{ {{x= \frac{6-y}{2} } \atop {x= \frac{2+y}{2} }} \right.$

$\frac{6-y}{2} = \frac{2+y}{2}$

$2(6-y) = 2(2+y)$

$12-2y = 4-2y$

$-2y+2y = 4 - 12$

$-4y = -8$

$y = \frac{-8}{-4} = \frac{8}{4} = 2$

${x= \frac{6-2}{2}=\frac{4}{2}=2$

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$\left \{ {{x-y=6} \atop {x+y=14}} \right.$

$\left \{ {{x = 6+y} \atop {x = 14-y}} \right.$

$6+y=14-y$

$y+y = 14 - 6$

$2y = 8$

$y = \frac{8}{2} = 4$

$x = 6+4 = 10$

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$\left \{ {{5x+y=8} \atop {4x+y=6}} \right.$

$\left \{ {{5x = 8-y} \atop {4x = 6-y}} \right.$

$\left \{ {{x= \frac{8-y}{5} } \atop {x= \frac{6-y}{4} }} \right.$

$\frac{8-y}{5} = \frac{6-y}{4}$

$4(6-y) = 5(8-y)$

$24-4y = 40-5y$

$-4y+5y = 40 - 24$

$y = 16$

$x= \frac{8-16}{5}=\frac{-8}{5}= -1,6$