3.4 SAT Math - Elimination

To use this method on the SAT math section, you simply line up your two equations and add or subtract them together to get rid of one variable, then substitute that information into one of the equations to solve for the second variable. 

Elimination Example

If 2x + 5z = 18 and 10x - 5z = 30, what is z?
Line up the two equations like they were numbers:

Then add each column:

You’ve now eliminated one variable by getting it to zero, so you can now solve for x:

12x = 48
x = 4

Substitute that number into one of the two equations to solve for the other.

2x + 5z = 18
2•4 + 5z = 18
8 + 5z = 18
5z = 10
z = 2

So z = 2 and x = 4.

Sometimes, if you want to use elimination, you will need to multiply one or even both equations through by an integer in order to create numbers that will eliminate nicely.

Example:

If 4x + 6y = 6 and 5x - 4y = 13, what is y?

If added or subtracted together, neither of these variables will disappear, so we’re going to multiply the first equation through by 2 and the second equation through by 3 to get a common multiple of 12 for y.

Now it will be much easier to put them on top of each other and eliminate the y:

x = 3

Now you can plug that into either equation and solve for y:

4x + 6y = 6
4•3 + 6y = 6
12 + 6y = 6
6y = -6
y = -1