Solving Systems by Elimination

Algebra Foundation

Algebra 1

Study expressions, equations, inequalities, functions, linear models, systems, polynomials, quadratics, and exponential growth with original explanations and worked examples.

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Algebra 1 · Unit 6 · Topic 6.3

Solving Systems by Elimination

Elimination adds equivalent equations to cancel a variable.

Definition and explanation

Elimination adds equivalent equations to cancel a variable. Multiplying an entire equation by a nonzero number first can produce opposite coefficients without changing its solutions.

Worked example

Solve 2x + 3y = 19 and 4x − 3y = 5. Adding gives 6x = 24, hence x = 4. Substitution in the first equation gives 8 + 3y = 19, so y = 11/3; the second equation also gives 5.

Common mistake

When multiplying an equation, multiply every term on both sides, including the constant.

Key takeaway

Elimination adds equivalent equations to cancel a variable.

Explain each step of the worked example, then check the units, signs, and conditions that apply.

Further reading

Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.