# ACT Practice Math Questions: Systems of Equations

You’re almost guaranteed to run across a problem or two dealing with systems of equations on the ACT Math exam. The following practice questions will test your skills at solving these tricky problems.

## Practice questions

- What is the value of
*a*in the (*a*,*b*) solution to the following system of equations?

- What is the value of
*y*in the following system of equations?

## Answers and explanations

- The correct answer is Choice
**(E).**The question asks you to solve for

*a*, so you need to eliminate the*b*values from the system. Because both equations are equal to*b*, you can set the expressions on the right sides of both equations equal to each other and solve for*a*: - The correct answer is Choice (
**E).**To solve a series of equations, you must cancel out one of the variables. Because the question asks that you find

*y*, it makes sense to cancel out*x*in order to isolate*y*. To do this, multiply the bottom equation by –4 and stack the two equations like this:When you add the equations, the

*x*terms cancel, the*y*terms add to 6*y*, and the sum of the right side of the equation is –60: 6*y*= –60. When you solve for*y*, you get –10.