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.
- 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 6y, and the sum of the right side of the equation is –60: 6y = –60. When you solve for y, you get –10.