ACT · Intermediate Algebra · Systems of equations and matrices
Question act-q-00382
Medium Multiple choice Calculator OK
The question
Consider the system of equations:
1x + 1y = -3
3x − 1y = -9
What is the value of x?
- -2
- 0
- -4
- -3
Show answer & worked solution
Answer: -3
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 = -3 and y = 0.
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.