ACT Practice Math Questions: Working with Multiple Variables

As if one variable weren't enough, the ACT Math exam will sometimes throw multiple variables into some of its algebra questions. The following practice questions test your skills with using substitution to solve for the variables a and b, and rearranging an equation to solve it in terms of y – x.

Practice questions

1. If a is five greater than b, and the sum of a and b is –15, then b² =

   A. 100 B. 64 C. 25 D. 20 E. 0

2. If then y – x =

Answers and explanations

1. The correct answer is Choice (A).
   Set up equations from the wording of the question: a = 5 + b and a + b = –15. Substitute the value of a in the first equation for a in the second equation and solve for b:

   

   So b² = 100.

2. The correct answer is Choice (D).
   Get the terms that have y and x in them on one side and all the terms that have nothing to do with y and x on the other side: