6x + 7y = -9
-4x - 5y = 5
We can use either substitution or elimination. I prefer substitution so I will explain it that way. You can use elimination as well.
We can solve for x first so we will need to substitute y in terms of x.
6x + 7y = -9
7y = -9 - 6x
y = (-9 - 6x)/7
Plugging this into the other equation:
-4x - 5[(-9 - 6x)/7] = 5
-4x + (45 + 30x)/7 = 5
-28x + 45 + 30x = 35
2x + 45 = 35
2x = - 10
x = -5
Insert this into the other equation to solve for y.
6(-5) + 7y = -9
-30 + 7y = -9
7y = 21
y = 3
Your answer should be (-5, 3). Hope this helps!