Answer:
One solution at (12, -9).
Step-by-step explanation:
We could just graph this system, which would be really easy, and count the number of intersections, but I will show you the algebraic way so you can understand it better!
Remember that two linear equations (for these are linear) can only have no solutions if they're parallel, infinite if they're the same line, and one if they cross at only one point. Two lines can't even have 2 solutions; that would be impossible.
Let's solve this with elimination. Multiply the top equation by 3 and the bottom equation by 2 so we can cancel the x's.
3( 2x + 3y = -3 ) -> 6x + 9y = -9
2( 3x + 5y = -9 ) -> 6x + 10y = -18
So our new equations are below. (If they had been the same equation, they would have been parallel and had infinite solutions!) Subtract them from one another to cancel the x's.
6x + 9y = -9
- 6x + 10y = -18
-----------------------
0x - y = 9
-y = 9
y = -9
Plug y back in to get x.
2x + 3y = -3
2x + 3(-9) = -3
2x - 27 = -3
2x = 24
x = 12
We have one solution at (12, -9).
