y= x-7

3x+6y=-6

I don't understand how to solve for the x-variable.

use substituion

in the 2nd
3x + 6y = -6
3x + 6(x-7) = -6
3x + 6x - 42 = -6
9x = 36
x = 4

put that back into y = x-7 to get
y = 4-7 = -3