Solving Systems by Substitution

Algebra Foundation

Algebra 1

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

Learn with original explanations and worked examples. OpenStax Elementary Algebra 2e was consulted for topic coverage.

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Algebra 1 · Unit 6 · Topic 6.2

Solving Systems by Substitution

Substitution replaces a variable in one equation with an equal expression from another equation.

Definition and explanation

Substitution replaces a variable in one equation with an equal expression from another equation. Solve the resulting one-variable equation, then recover and check the other variable.

Worked example

Solve y = 3x − 2 and x + y = 10. Substitute to get x + 3x − 2 = 10, so x = 3. Then y = 7. Check: 3 + 7 = 10 and 7 = 3(3) − 2.

Common mistake

Substitute the full expression, including its signs and constant terms.

Key takeaway

Substitution replaces a variable in one equation with an equal expression from another equation.

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.