Linear Equations Quiz
15 questions · free · new questions every attempt · Updated September 26, 2026
A linear equation has a variable to the first power, and solving it means isolating that variable. The method is always the same: undo operations in reverse order and keep both sides balanced. This quiz builds from two-step equations to variables on both sides, equations with fractions and simple systems.
What this quiz covers
- Solving two-step equations
- Variables on both sides of the equation
- Equations containing fractions
- Solving a system by adding equations
- Finding a y-intercept from a slope and a point
- Checking a solution by substitution
How to prepare
Whatever you do to one side, do to the other. Move variable terms to one side and numbers to the other, then divide. Always check by substituting your answer into the original equation; it takes ten seconds and catches most mistakes.
Sample questions with answers
These five questions show the style. Your quiz above will have different numbers each time.
- Solve for x: 9x + 11 = 65
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6. Subtract 11: 9x = 54. Divide by 9: x = 6.
- Solve for x: 5x + (-7) = 4x + -13
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-6. Subtract 4x from both sides: 1x + -7 = -13. Then x = (-13 − -7) ÷ 1 = -6.
- Solve for x: x/5 + 4 = 11
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35. Subtract 4: x/5 = 7. Multiply by 5: x = 35.
- Solve the system: x + y = 11 and x − y = 1. What is x?
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6. Add the equations: 2x = 12, so x = 6 (and y = 5).
- A line has slope 4 and passes through (1, -2). What is its y-intercept?
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-6. y = 4x + b, so b = -2 − 4 × 1 = -6.
Frequently asked questions
How do I solve for x?
Isolate x by reversing the operations applied to it: subtract or add first, then divide or multiply.
What if x is on both sides?
Subtract the smaller x-term from both sides so the variable appears once, then continue as usual.
What is a system of equations?
Two or more equations with the same unknowns. You find values that satisfy all of them at once.
Keep practising
How to Solve Quadratic Equations8 min read
Multiplication Quiz15 questionsFractions Quiz15 questionsDecimals Quiz15 questionsReviewed September 26, 2026 by the SolveCalcPro editorial team. Questions are generated from tested formulas. Spot a mistake? Tell us.