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Systems by Substitution

A free Algebra I lesson from the “Systems of Linear Equations and Inequalities” unit, with a worked example and practice problems including step-by-step solutions.

Substitution works best when one equation already tells you what a variable equals. Replace that variable in the other equation, solve, then substitute back. In Systems of Linear Equations and Inequalities, students need more than a memorized rule: they need to recognize the structure, select a method, carry out the algebra cleanly, and interpret the answer in a graph, table, equation, or real context. The expanded practice now mixes skill fluency, transfer questions, and cumulative review so the lesson builds durable Algebra I readiness.

What you'll learn

Why it matters: Substitution helps when one relationship already gives a value or rule that can be dropped into another relationship, like a known price or an isolated measurement.

Worked example

Problem. Solve y = 2x + 1 and x + y = 10.

  1. Substitute 2x + 1 for y in x + y = 10.
  2. x + 2x + 1 = 10, so 3x = 9 and x = 3.
  3. y = 2(3) + 1 = 7, so the solution is (3, 7).
  4. Connect the result back to Systems by Substitution so the method and meaning are both clear.

Answer: (3, 7)

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. Solve y = x + 2 and x + y = 8. Enter x.

Show solution
  1. Substitute x + 2 for y.
  2. x + x + 2 = 8, so x = 3.

Answer: 3

2. For y = x + 2 and x + y = 8, enter y.

Show solution
  1. Use x = 3.
  2. y = 3 + 2 = 5.

Answer: 5

3. Which equation is easiest to substitute into 3x + y = 11?

Choices: y = 2x - 1 · 3x + 2y = 14 · x + y = 8 · 4x - y = 2

Show solution
  1. y is already isolated.

Answer: y = 2x - 1

4. Solve y = 4 and 2x + y = 14. Enter x.

Show solution
  1. Substitute y = 4.
  2. 2x + 4 = 14, so x = 5.

Answer: 5

5. Solve x = y + 1 and x + y = 9. Enter y.

Show solution
  1. Substitute y + 1 for x.
  2. y + 1 + y = 9, so 2y = 8 and y = 4.

Answer: 4

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