We will multiply the given equations so that the x component is cancels out upon addition...
-3(2x-3y=9)+2(3x+2y=-6) perform indicated operations.
(-6x+9y=-27)+(6x+4y=-12) which is equal to:
13y=-39 divide both sides by 13
y=-3, making 2x-3y=9 become:
2x-3(-3)=9
2x+9=9 subtract 9 from both sides
2x=0 divide both sides by 2
x=0
So the solution to the system is the point (0,-3)...
You can check with the two original equations...
2(0)-3(-3)=9, 9=9
3(0)+2(-3)=-6, -6=-6