How do you solve linear equations using linear combinations?

Solving linear equations using linear combinations basically means adding several equations together so that you can cancel out one variable at a time.

For example, take the following two equations: x+y=5 and x-y=1

If you add them together you get 2x=6 or x=3

Now, put that value of x into the first original equation, 3+y=5 or y=2

Therefore your solution is (3, 2)

But problems are not always so simple.

For example, take the following two equations: 3x+2y=13 and 4x-7y=-2 to make the "y" in these equations cancel out, you must multiply the whole equation by a certain number.