ACT · Intermediate Algebra · Systems of equations and matrices
Question act-q-00389
Medium Multiple choice Calculator OK
The question
Consider the system of equations:
1x + 5y = 25
3x − 2y = 7
What is the value of x?
- 6
- 4
- 5
- 4
Show answer & worked solution
Answer: 5
Worked solution. Multiply the first equation by 3 and the second by 1, 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 a moderate position in the section — solidly within the range that separates a 600-band student from a 700-band student. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.