What is the solution of this linear system ? 3x + y = -2 y = -x +4

The answer is as follows 
x = -3
y = 7

There are a few ways to do this but lets do it the following way.

3x + y = -2
y = -x +4 <--- turn this to standard form

y = -x + 4
x + y = 4

3x + y = -2
x + y = 4 < Times this by -3 to cancel out

3x + y = -2
-3(x + y) = 4 * -3

3x + y = -2
-3x -3y =  -12

+ y = -2
 -3y =  -12

-2y = - 14

-2y / -2 = - 14 / -2

y = 7

Now that we found y we can insert 7 into the y position in one of the equation. For instance 

y = -x +4
7 = -x + 4
7 = -x + 4
-4 + 7 = -x
3 =  -x
x = -3