Solve for an unknown in one or two variables, and know what the solution actually means — a point, a line, or no solution at all. Every question comes with a written walkthrough of each solving step.
Subtracting a term from one side but forgetting to subtract it from the other undoes the whole equation, not just that one term.
When isolating a variable across a sum, every term on that side needs the same operation applied — not just the term with the variable in it.
An equation that reduces to something false, like 3 = 5, isn't an error to fix — it's the answer. Solving further just reintroduces a mistake trying to force a solution that doesn't exist.
Straight from the bank — one per difficulty tier. Reveal the answer to see the explanation you'd get in a real session.
Solve for x: 3x − 7 = 14
B — 7. Add 7 to both sides: 3x = 21, then divide by 3: x = 7. 21 (D) is the value of 3x, left un-divided — a common stopping point when the final step gets skipped.
Solve for x: 5x − 3 = 2x + 12
B — 5. Collect the variable terms on one side by subtracting 2x from both sides: 5x − 2x − 3 = 12, giving 3x − 3 = 12. Add 3 to both sides: 3x = 15, so x = 5. 15 (D) is 3x left un-divided by 3 — the same "forgot the last step" trap as the foundation tier, just one layer deeper.
Solve the system: 2x + 3y = 12 and x − y = 1. Find x + y.
C — 5. Solve by substitution: from x − y = 1, x = y + 1. Substitute into 2x + 3y = 12: 2(y + 1) + 3y = 12 → 5y + 2 = 12 → y = 2, so x = 3, and x + y = 5. 4 (B) is what you get from mixing up x and y partway through the substitution — a common slip once two steps are chained together in a system.
Linear equations are pure procedure — the fastest way to raise this score is running enough reps that each step becomes automatic, not something you re-derive.
Show each inverse operation as its own line, including on both sides of the equation. Untimed practice is where you catch the sign errors that speed hides.
Move to timed sessions once your steps are error-free. Systems take longer than single-variable equations, so budget accordingly.
Combine linear equations with quadratic equations in a mock — quadratics often start with a linear step you already know.
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