Question

Найдите решение системы уравнений {
х + у = 2,
х − у = −6

Answer 1

$\left \{ {{x+y=2} \atop {x-y=-6}} \right. \\\left \{ {{x+y=2} \atop {x=-6+y}} \right. \\-6+y+y=2\\2y=8\\y=4\\x=-6+4=-2$

(-2;4)

Answer 2

$\left\{\begin{array}{ccc}x+y=2\\x-y=-6\end{array}\right\;\;\;\; \Longrightarrow \;\;\;\; \left\{\begin{array}{ccc}x=2-y\\-y+(2-y)=-6\end{array}\right \\\\\\ -y+(2-y)=-6 \\ 2 - 2y = -6 \\ -2y = -6 - 2 \\ -2y = -8 \\\\ y = \dfrac{-8}{-2} \\\\ y = 4 \\\\\\ x = 2 - 4 \\ x = -2$

Ответ: (-2; 4)