SAT · Heart of Algebra · Systems of two linear equations
Question sat-q-00037
Medium Multiple choice Calculator OK
The question
Consider the system of equations:
5x + 2y = 12
4x − 1y = 20
What is the value of x?
- 5
- 4
- -4
- 3
Show answer & worked solution
Answer: 4
Worked solution. Multiply the first equation by 4 and the second by 5, then subtract to eliminate x — or, more easily here, add or subtract directly. Solving the system gives x = 4 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
A staple of every SAT form. The system may be presented in standard form, in slope-intercept form, or as a word problem you must translate. Some items ask only for one variable's value; others ask for the sum, product, or difference of the two variables. A small fraction of items ask for the number of solutions (one, none, or infinitely many) without solving.
You will see a question shaped like this one on roughly every other official SAT 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.