You can use the substitution method.
Let's choose the second equation in terms of y (which is much easier),
-y = 4 - x
y = -4 + x
y = x - 4
Substitute this to the first equation to get the value of x.
-5x + 3(x - 4) = 6
-5x + 3x - 12 = 6
-2x = 6 + 12
-2x = 18
x = -9
Substitute it to the first equation that we have used.
y = -9 - 4 = -13
