Solve the system of equations using elimination. 2x – 3y = 9 and 3x + 2y = –6

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