Question 149514
Systems are really simple, sometimes people let them get the best of them...

What you want to do is make a variable in one equation, cancel out the same variable in the other equation

For example... y and -y, 2x and -2x, 3z and -3z

But remember! what you do to one variable, you have to do to the WHOLE equation...

With this equation, let's pick 2x and 4x...

We're going to multiply the 2x+y=12 equation by (-2) so that 2x becomes the OPPOSITE of 4x... 

Like this...

(2x+y=12)*(-2)
-4x-2y=-24

now, we can add the other equation to it...

  -4x-2y=-24
+  4x-3y= 9
_____________
     -5y= -15
Divide both sides by "-5"
       y= 3

Now you subsitute 3 for y in the original problem.

2x +  y = 12
2x + (3)= 12
Subtract 3 from both sides
2x + 3 (-3) = 12 (-3)
2x= 9
 x= 9/2

Now you've solved the system!! Good luck!