Skyler, the trick to solving by elimination is to get either the x's or the y's to be opposites so that you can add the equations and eliminate that variable.
3x + 4y = 12
2x - 4y = 13
5x = 25
x = 5
Then plug the value you find into one of the equations and solve for the other variable.
What if nothing matches up? Multiplying an equation times anything does not change the equation.
3x + 4y = 55
2x + 5y = 74
Nothing matches, but we can find a way.
-2(3x + 4y) = -2(55)
3(2x + 5y) = 3(74)
-6x - 8y = -110
6x + 15y = 222
7y = 112
y = 16
Hope this helps!
