If you would like to find the linear system with the solution (6, 6), you can do this using the following steps:
(6, 6) = (x, y)
x = 6
y = 6
4x - 3y = -1 ... 4 * 6 - 3 * 6 = -1 ... 24 - 18 = -1 ... 6 = -1
-2x + y = -3
_________
x + y = 12 ... 6 + 6 = 12 ... 12 = 12
3x - 2y = 6 ... 3 * 6 - 2 * 6 = 6 ... 18 - 12 = 6 ... 6 = 6
The correct result would be x + y = 12, 3x - 2y = 6.