Combination, continued

However, most of the time, the two equations won’t line up as cleanly as they did in the previous example.

Sometimes it’s necessary to multiply an equation by a number in order to get a variable to cancel out.

For example, if you add the equations 3x + 4y = 12 and x + 2y = 10 together, neither x nor y will cancel out. But if you multiply both sides of the second equation by –2, you’ll get somewhere:

And then adding the new second equation to the original first equation:

The y drops out. Remember, you can multiply both sides of any equation by any number other than zero, and the equation will still be true. This is very helpful in combination problems.