Skill: systems-equations

Systems Practice

An endless supply of never-repeating systems problems: solve by substitution and elimination, read solutions off graphs, pick the most efficient method, classify systems, and verify candidates.

1 Practice

Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss walks you through the full solution.

Score 0 · Streak 0 · Problem 0

Score counts first-try correct answers. Streak counts consecutive correct answers.

Problem

How to enter answers

Solutions: type the ordered pair (3, 1) — parentheses optional.
Classify: type one solution, no solution, or infinitely many.
Verify/method: type yes / no, or substitution / elimination / graphing.

2 What you’ll practice

Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.

Solve it

Substitution-ready and elimination-ready systems with integer solutions.

y = 2x−5, 3x+y = 10 → (3, 1)

Choose & classify

Pick the smartest method; name one/none/infinite.

same slope, new intercept → no solution

Verify & apply

Test candidates and solve word problems.

(2,−1) in both? → yes

3 Watch out for these

The mistakes students make most often on these problems.

1. Forgetting y

Wrong: “the solution is x = 3.” Right: (3, 1) — ordered pair, both coordinates.

2. Partial multiplication

Wrong: multiplying one term to align. Right: multiply the entire equation.

3. Wrong method

Wrong: graphing when substitution is exact. Right: isolated variable → substitution.

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