Question

Pelo método da substituição:

X+Y = -6
2X-Y= -2

Answer 1

Tem-se o sistema de equações:

$\left\{\begin{array}{l}\sf x+y=-6\ (I)\\\sf 2x-y=-2\ (II)\end{array}$

Escolhendo a equação (I) para resolver pelo método de substituição:

$\sf x+y=-6\\\\\boxed{\sf x=-6-y}$

Substituindo o valor de x na equação (II):

$\sf 2x-y=-2\\\\\sf 2(-6-y)-y=-2\\\\\sf -12 -2y-y=-2\\\\-12-3y=-2\\\\\sf-3y=-2+12\\\\-3y=10\\\\\sf 3y = -10\\\\\sf y = \dfrac{-10}3\\\\\\\boxed{\sf y=-\dfrac{10}3}$

Substituindo o valor de y na equação (I):

$\sf x+y=-6\\\\\sf x+\left(-\dfrac{10}3\right)=-6\\\\\\\sf x -\dfrac{10}3 = -6\\\\\\\sf x = -6 + \dfrac{10}3\\\\\\\sf x = -\dfrac{18}3+\dfrac{10}3\\\\\\\sf x = \dfrac{-18+10}3\\\\\\\sf x = \dfrac{-8}{3}\\\\\\\boxed{\sf x = -\dfrac83}\\\\\\\\\boxed{\sf (x, y) = \left(-\dfrac83, -\dfrac{10}3\right)}$

Bons estudos.