What is a system of equations?

Two or more equations solved together; the solution makes every equation true at the same time.

Substitution or elimination, which should I use?

Substitution is easy when one equation is already solved for a variable; elimination shines when coefficients line up.

Systems of Equations · Grades 10–10

Systems of Equations Worksheets

One point has to satisfy both equations at once. Worksheets for solving systems by substitution and by elimination.

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What it is

A system of equations is two equations that must be true at the same time. The solution is the (x, y) that satisfies both.

Why it matters

Two phone plans with different monthly rates and fees cross over at some usage level — finding that crossover point is a system of equations, which is exactly the comparison this skill is built to handle.

How to do it

Line up the two equations.
Use substitution or elimination to remove one variable.
Solve for the remaining variable, then back-substitute for the other.

Examples by level

Beginner4x + 3y = -35; 3x + 2y = -25 =Answerx = -5, y = -5
Intermediate4x + 2y = -32; 2x + 2y = -22 =Answerx = -5, y = -6
Advanced6x − 7y = 72; 5x + 2y = 13 =Answerx = 5, y = -6

Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.

Common mistakes

Solving for one variable but forgetting the other.
Sign errors during elimination.
Not checking the solution in both equations.

Tips

Check your solution in BOTH equations.
Elimination works well when a variable's coefficients match.

For parents

Always plug the answer back into both original equations, it's the quickest way to catch a slip.

For teachers

Show substitution and elimination on the same system so students choose the efficient method.

Key vocabulary

system: two or more equations solved together
solution: the values that satisfy every equation

Frequently asked questions

What is a system of equations?: Two or more equations solved together; the solution makes every equation true at the same time.
Substitution or elimination, which should I use?: Substitution is easy when one equation is already solved for a variable; elimination shines when coefficients line up.

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