3+y=-x

-5x+2y=8

solve in standard form

First answers x+y = - 3

5x-2y = - 8

Rewrite in standard form

x+y = - 3

the second equation is already in standard form.

now, solve for x

x = - 3-y

substitute into the other equation and solve for y

-5 (-3 - y) + 2y = 8

15 + 5y + 2y = 8

15 + 7y = 8

7y = - 7

y = - 1

now substitute into the original equation

x + - 1 = - 3

x = - 2

answer (-2, - 1)