Heart of Algebra

Systems of Linear Equations

Solve two-variable systems by substitution and elimination. Each question below has a complete worked solution.

This collection of 25 SAT math practice questions on systems of linear equations is sequenced by difficulty so you can warm up on routine problems and progress to the kind of question that separates a competitive math score from an elite one. The first eight problems are calibrated to roughly easy College Board difficulty — the kind that appears in the first third of the math section. The next ten are medium difficulty: the bread-and-butter of the middle of the test. The final seven push into hard territory, where the question writers add an extra step, hide a sign change, or ask for an unrelated expression after you solve.

Work each question on paper before you look at the worked solution. The solution is there to confirm or correct your work, not to lead you. If you cannot start a problem after 30 seconds, mark it and come back; if you cannot finish after 90 seconds, look at the first line of the solution and try again. That structured exposure to the worked solution — not a glance, not a copy — is the most reliable way to convert a missed question into a permanent skill.

#QuestionDifficultyBand
1 If 2x + 4y = -10 and 3x - 2y = -15, what is the value of x + y? easy 400-500 Open
2 If 1x + 4y = 2 and 2x - 3y = 15, what is the value of x + y? easy 400-500 Open
3 If 4x + 4y = -8 and 5x + 3y = -10, what is the value of x + y? easy 400-500 Open
4 If 1x + 5y = 25 and 4x - 4y = -20, what is the value of x + y? easy 400-500 Open
5 If 3x + 2y = 12 and 4x - 3y = 33, what is the value of x + y? easy 400-500 Open
6 If 2x + 1y = -9 and 1x - 4y = -18, what is the value of x + y? easy 400-500 Open
7 If 2x + 5y = -27 and 3x + 4y = -23, what is the value of x + y? easy 500-600 Open
8 If 4x + 4y = -4 and 2x + 4y = -10, what is the value of x + y? easy 500-600 Open
9 If 5x + 5y = 30 and 4x - 3y = 24, what is the value of x + y? medium 500-600 Open
10 If 5x + 5y = -25 and 2x - 4y = -10, what is the value of x + y? medium 500-600 Open
11 If 3x + 5y = -11 and 1x - 5y = 3, what is the value of x + y? medium 500-600 Open
12 If 1x + 4y = -21 and 4x + 5y = -40, what is the value of x + y? medium 500-600 Open
13 If 5x + 2y = -40 and 1x + 5y = -31, what is the value of x + y? medium 600-700 Open
14 If 3x + 5y = -10 and 5x - 3y = 40, what is the value of x + y? medium 600-700 Open
15 If 1x + 4y = -5 and 2x - 2y = -10, what is the value of x + y? medium 600-700 Open
16 If 3x + 1y = 3 and 4x - 5y = -34, what is the value of x + y? medium 600-700 Open
17 If 4x + 1y = 26 and 1x + 5y = 35, what is the value of x + y? medium 600-700 Open
18 If 5x + 4y = -31 and 2x + 3y = -18, what is the value of x + y? medium 600-700 Open
19 If 5x + 3y = -19 and 3x - 3y = -21, what is the value of x + y? hard 600-700 Open
20 If 1x + 4y = -20 and 3x + 4y = -20, what is the value of x + y? hard 700-800 Open
21 If 3x + 1y = 16 and 5x + 3y = 24, what is the value of x + y? hard 700-800 Open
22 If 3x + 5y = -17 and 4x - 2y = 12, what is the value of x + y? hard 700-800 Open
23 If 3x + 2y = 12 and 3x - 3y = 12, what is the value of x + y? hard 700-800 Open
24 If 5x + 2y = 7 and 4x - 3y = 24, what is the value of x + y? hard 700-800 Open
25 If 3x + 2y = 1 and 3x + 1y = 2, what is the value of x + y? hard 700-800 Open