ACT · Intermediate Algebra · Systems of equations and matrices
Question act-q-00386
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The question
Consider the system of equations:
5x + 4y = 41
5x − 5y = 5
What is the value of x?
- 4
- 4
- 6
- 5
Show answer & worked solution
Answer: 5
Worked solution. Multiply the first equation by 5 and the second by 5, then subtract to eliminate x — or, more easily here, add or subtract directly. Solving the system gives x = 5 and y = 4.
Why each wrong choice is wrong. One distractor is the value of y — students who solve the system but forget which variable was asked for. Two others are off-by-one slips.
Test-day tactic. Decide substitution vs. elimination before doing algebra. With both equations in standard form, elimination is almost always faster.
About this question type
Items test 2-by-2 linear systems and the basics of matrix addition, subtraction, and scalar multiplication.
You will see a question shaped like this one on roughly every other official ACT form, typically at an early position in the section, where missing them carries an outsize penalty because the curve assumes everyone in your band gets them right. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.