Question

If you wanted to eliminate the y variable by adding the two equations in the following system, what could be your first step?

2x − 4y = 6
3x − y = 12

Add the two equations together

Multiply the first equation by −4

Multiply the second equation by −4

Multiply the second equation by 4

Answer 1

You want to do something to cause one of the terms to cancel out the corresponding term in the other equation when added together. Adding them together as is won't do, because neither the x nor y terms are equal magnitude but opposite in sign. Multiplying the second equation by -4 will give you -12x + 4y = -48, and if you add that to the first equation, the -4y will cancel out the 4y, so that is your choice. Note that you could also multiply the second equation by 4 and subtract the second equation from the first to get the same result (because subtraction is the same as multiplying the second equation by -1 and adding).

After multiplying the second equation by -4 you would have:

2x - 4y = 6
-12x + 4y = -48
---------------
-10x = -42

x = 4.2
and then you substitute that value into either equation and solve for the value of y.