Quick answer: Elimination makes the coefficients of one variable equal or opposite so subtraction or addition removes it. Multiply every term of an equation when scaling it.
Worked example
Solve 2x + 3y = 17 and 3x − 2y = 6.
- Multiply the first equation by 2: 4x + 6y = 34.
- Multiply the second by 3: 9x − 6y = 18.
- Add: 13x = 52, so x = 4.
- Use 8 + 3y = 17 to get y = 3.
Check the result
The second equation gives 12 − 6 = 6; both original equations hold.
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Common mistake to avoid
Subtracting equations with opposite coefficients doubles the variable instead of eliminating it. Choose addition or subtraction from the signs.
Try it yourself
1. Solve x + y = 8 and x − y = 2. 2. Solve 2x + y = 7 and x − y = 2.
Answers and reasoning
1. Add to obtain x = 5, then y = 3. 2. Add to obtain 3x = 9, so x = 3, y = 1.
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