1)  Multiply one or both of the equations by a constant to obtain coefficients
that differ only in sign for one of the variables.

2) Add the revised equations from Step 1. Combining like terms will eliminate
one of the variables. Solve for the remaining variable.

3) Substitute the value obtained in Step 2 into either of the original equations and
solve for the other variable.

2x - 4y = 13  and  4x - 5y = 8

Now, place them on top of each other so that like variables match up and it is easy
to work. Pick one variable that you want to eliminate. In this case we will use the x
variable since it is easier.

2x - 4y = 13    times 2    -4x + 8y = -26 (make sure to multiply everything)

4x - 5y = 8    
-4x + 8y = -26

Now that the x's cancel out, the rest is simple math.  
You should end up with: 3y = -18 which means  y = -6

Now take this, and plug it into either of the equations you started with to find the x
value.

2x - 4(-6) = 13
2x + 24 = 13
x = -11/2

So the solution is  (-11/2 , -6)

Now put your skills to use..... Solve the following using linear combination.

1. 3x + 5y = -16   and  3x - 2y = -9

2. -6x + 5y = 4  and  7x - 10y = -8

Answers:  1. (-11/3, -1)   2. (0, 4/5)