ACT Practice Math Questions: Systems of Equations

By Lisa Zimmer Hatch, Scott A. Hatch

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

  1. What is the value of a in the (a, b) solution to the following system of equations?
    ACT_1501
  2. What is the value of y in the following system of equations?
    ACT_1502

Answers and explanations

  1. 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:

    ACT_1503

  2. 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:

    ACT_1504

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