Substitution Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Substitution.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Replacing every occurrence of a variable or sub-expression with an equivalent value or expression throughout a problem.

If y = 2x, you can write 2x everywhere you see y—they're the same.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Substitution exploits equality—equal things can replace each other.

Common stuck point: You must substitute the value into EVERY occurrence in the expression, not just the first one you see.

Sense of Study hint: Use parentheses around the entire expression you are substituting in, then simplify step by step.

Worked Examples

Example 1

easy
If y = 3x + 1 and x = 2, find y.

Solution

  1. 1
    Replace x with 2 in the expression: y = 3(2) + 1.
  2. 2
    Compute: y = 6 + 1 = 7.
  3. 3
    Substitution replaces a variable with its known value.

Answer

y = 7
Substitution means replacing a variable with an equivalent value or expression. Here we replace x with 2 to find the corresponding y.

Example 2

medium
If y = x + 3 and 2x + y = 9, use substitution to solve for x.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Evaluate a + 2b when a = 5 and b = -1.

Example 2

medium
If u = 2v - 1 and 3u + v = 11, find v.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

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