x - 3y = -6.......x = 3y - 6
so we sub in 3y - 6 in for x in the other equation
-4x + 9y = 9
-4(3y - 6) + 9y = 9
-12y + 24 + 9y = 9
-12y + 9y = 9 - 24
-3y = - 15
y = -15/-3
y = 5
x = 3y - 6
x = 3(5) - 6
x = 15 - 6
x = 9
solution is (9,5) <===
======================
4x - 3y = 11 .....multiply by 3
3x - 5y = -11...multiply by -4
-----------------
12x - 9y = 33 (result of multiplying by 3)
-12x + 20y = 44 (result of multiplying by -4)
-----------------add
11y = 77
y = 77/11
y = 7
4x - 3y = 11
4x - 3(7) = 11
4x - 21 = 11
4x = 11 + 21
4x = 32
x = 32/4
x = 8
solution is (8,7) <===