Solving Systems of Linear Equations by Addition Examples

If we want to solve this system by eliminating the variable x, what number should we multiply the second equation by?

The coefficient of x in the first equation is 4. The coefficient of x in the second equation is 2. In order to get the coefficients on x to be additive inverses, we can multiply the second equation by -2:

-4x – 8y = -34

Replacing the second equation with this new version gives us the system

in which the coefficients of x are additive inverses. Now we can eliminate. It's Elimsanity!

For the following system of equations, eliminate the variable y from the system to get an equation involving only x.

Multiply the first equation by 4 and the second equation by -3 to find

then add for -5x = 17. There are other correct ways to eliminate x, but they should all lead to the solution . No way of avoiding the fraction, sorry. There are plenty of incorrect solutions that lead elsewhere, however, if that makes you feel any better.