Quote: 5x+3y=-6
10x+9=-12
Solve for x and y
There are 2 main ways of doing this
1) solving for one variable in terms of the other
5x+3y=-6
y = 1/3(-6-5x)
Now plug this into the 2nd equation
10x + 9y = -12 (this isn't what you wrote but I assume it's what you meant)
10x + 9(1/3(-6-5x)) = -12
10x - 3(6+5x) = -12
-5x - 18 = -12
-5x = 6
x=-6/5
plugging this into the equation for y
y = 1/3(-6-5(-6/5))
y = 1/3(-6 + 6) = 0
2) the elimination method, you add or subtract multiples of one equation from the other.
5x + 3y = -6
10x + 9y = -12
subtract twice the first equation from the second equation
(10-2*5)x + (9-2*3)y = -12 - (2*-6)
3y = 0
y = 0;
plug this into the first equation
5x + 0 = -6
x = -6/5
+6251 
