Multiply everything on the second equation by 2, and everything on the first one by -1.
[tex]2(2x+3y)=2(15)\\4x+6y=30[/tex]
[tex]-1(4x+2y)=-1(18)\\-4x-2y=-18[/tex]
Then you add the equations.
[tex]4x+6y=30\\-4x-2y=-18\\\\4y=12\\y=12/4\\y=3[/tex]
We substitute into the first equation (it could be the second) to find x:
[tex]4x+2y=18\\\\4x+2(3)=18\\4x+6=18\\4x=18-6\\4x=12\\x=12/4\\x=3[/tex]
Now, we substitute into the second equation (again, could be the first; just don't use the same equation in these 2 steps):
[tex]2x+3y=15\\2(3)+3(3)=15\\6+9=15\\15=15[/tex]
We are correct, so our answers should be:
[tex]x=3\\y=3[/tex]
