Systems of Linear Equations: SAT Practice Questions

126 official Systems of Linear Equations questions (Algebra) from the SAT Suite Question Bank. Pick any question from the list, or start with Question 1. Every question shows the answer and a full explanation, with step-by-step Desmos solutions available for most questions. It is free, and no account is needed.

Start with Question 1

What does Systems of Linear Equations test on the SAT?

Systems questions involve two linear relationships that must hold at the same time. The intersection can represent a numeric solution, a break-even point, or the values of model parameters.

Common question types

Solve a system algebraically or graphically
Build two equations from context
Determine whether a system has one, zero, or infinitely many solutions

Common traps

Solving for one variable and forgetting the other
Combining equations without aligning coefficients
Misinterpreting parallel or identical lines

Difficulty distribution

Start with the easier questions, then work toward the highest score bands.

Easy: 38
Medium: 46
Hard: 42
Extreme: 0

Start here

FoundationQuestion 8Easy SAT question IntermediateQuestion 2Medium SAT question ChallengeQuestion 125Hard SAT question

How do I improve at Systems of Linear Equations?

1Write both equations with clearly defined variables.
2Choose substitution or elimination based on the easiest coefficient.
3Verify the ordered pair in both original equations.

Desmos method

Graph both equations and select their intersection. Parallel distinct lines mean no solution, while the same line written twice means infinitely many solutions.

All 126 official questions

In the same order as the list on the left. Each one opens in practice mode.