In Linear Combination (also called elimination) you must get one of the variables to have the same number coefficient, but opposite signs. This is important because in this method you add the two equations together to try and eliminate a variable, and adding a -x and a x equals 0 x's.

Linear Combination is a good method to use when, the equations have a x or y value with the same coefficients for one of the variables or two coefficients that can easily be multiplied to be equal. For instance:
3x + 4y = 10
6x + 4y = 6
In this case, the y variable in both equations has a coefficient of 4. Now all you have to do is multiply all of one of the equations by -1 to make one of the 4y's a -4y.

It is still easy enough in this case, but a little more work is required:
3x + 4y = 14
6x - 2y = 8
This can easily be changed by multiplying the bottom equation by -2.

Now let's try one:

Let's use the 2nd example:

3x + 4y = 14
6x - 2y = 8

Multiple 2nd equation by 2  > 2(6x - 2y) = (8)2
Makes it  > 3x + 4y = 14
                  12x - 4y =16
Add the to equations together and solve  v
15x = 30
x = 2

Now you plug in the x value into one of the original equations and solve for y  v
3(2) + 4y = 14
4y = 20
y = 5

SOLUTION (Point of intersection):
(2,5)

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