SAT · Heart of Algebra · Systems of two linear equations
Question sat-q-00040
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The question
Consider the system of equations:
2x + 2y = -14
3x − 3y = -15
What is the value of x?
- -5
- -6
- -1
- -7
Show answer & worked solution
Answer: -6
Worked solution. Multiply the first equation by 3 and the second by 2, then subtract to eliminate x — or, more easily here, add or subtract directly. Solving the system gives x = -6 and y = -1.
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 the back end of the section, where the score gradient is steepest. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.