If we want to solve this system by eliminating the variable x, we need to multiply one of the equations by a number first. Which equation, and what number?

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 to find

-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!

Example 2

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.