You have the following system of equations:
-2x + y = 8
3x + y = -2
The previous system must be solved by substitution. Then, you proceed as follow:
You solve the first equation for y:
-2x + y = 8 add 2x both sides
y = 8 + 2x
You previous expression for y into the second equation, as follow:
3x + y = -2 replace y = 8 + 2x
3x + (8 + 2x) = -2 eliminate parenthesis
3x + 8 + 2x = -2 simplify similar terms left side
3x + 2x + 8 = -2
5x + 8 = -2 subtract 8 both sides
5x = -2 -8
5x = -10 divide by 5 both sides
x = -10/5
x = -2
Next, you replace the value of x into one of the given equation:
-2x + y = 8 replace x
-2(-2) + y = 8
4 + y = 8
y = 8 - 4
y = 4
Hence, the solution to the given system of equations is:
x = -2
y = 4