Solving Systems of Linear Equations
9-4The Addition-or-Subtraction Method
Overview
Add or subtract equations to eliminate one variable.
Key ideas
- Line up like terms.
- Add to cancel opposites; subtract to cancel matches.
- Solve, then back-substitute.
Worked examples
Example 1
Problem. x + y = 7 and x − y = 1.
Solution. Add: 2x = 8 → x = 4, y = 3.
Practice
Try each one. Click Show answer when ready.
- 1.
x + y = 10, x − y = 4.
- 2.
2x + y = 11, x − y = 1.
- 3.
3x + y = 12, 3x − y = 0.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Solve: 2x + 3y = 13 and 2x − y = 5.
- 2.
Solve: 3x + 2y = 12 and 5x − 2y = 4.