answer and shown work for 5x + y = 10 -x - y = -2

Solve first equation for y: 
5x+y=10
y=10-5x. Plug this equation into second equation

-x-(10-5x)=-2
-x-10+5x=-2
4x=8
x=2 (plug x into first equation)

5(2)+y=10
y=0