Solving Systems of Linear Equations
9-2The Substitution Method
Overview
Solve one equation for a variable, substitute into the other, solve, then back-substitute.
Key ideas
- Pick the easiest variable to isolate.
- Substitute its expression into the other equation.
- Solve, then find the other variable.
Worked examples
Example 1
Problem. y = 2x; x + y = 9.
Solution. x + 2x = 9 → x = 3, y = 6. (3, 6).
Practice
Try each one. Click Show answer when ready.
- 1.
y = x − 1; 2x + y = 8.
- 2.
x = y + 2; 3x + y = 14.
- 3.
y = 4x; x + y = 10.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Solve by substitution: 3x + y = 7 and y = 2x − 1.
- 2.
Solve by substitution: x + 2y = 8 and x = y + 2.