Systems of Equations Practice
An endless supply of never-repeating systems with instant feedback. Substitute when a variable is isolated, eliminate when coefficients line up — and always finish the point.
1 Practice
Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss earns a second hint; a third miss walks you through the full solution.
How to enter answers
- Your answer: an ordered pair like
(3, 7)—3,7andx=3, y=7work too. Fractions like(1/2, 3/2)are exact-friendly. - Special cases: type
no solutionfor parallel lines,infinitewhen both equations describe the same line.
2 What you’ll practice
Every problem is generated fresh from 12 templates across the skill — a problem never repeats until its whole pool is used up.
Substitution
One variable already isolated? Plug its expression into the other equation.
Elimination
Line the coefficients up, multiply if needed, add or subtract to wipe out a variable.
Special cases
Parallel lines (no solution) and the same line twice (infinitely many).
3 Watch out for these
The three mistakes students make most often here.
Wrong: answering “y = 2”. Right: back-substitute and write the full point: (3, 2).
Wrong: a sign slip passes because only the first equation was checked. Right: verify the point in both equations — that is the definition of a system solution.
Wrong: 0 = 0 → “no solution”. Right: false (0 = 5) → no solution; true (0 = 0) → infinitely many.