Remove one variable
Elimination combines equivalent equations so one variable cancels and a one-variable equation remains.
Learning goals
- Choose and create equal or opposite coefficients.
- Eliminate, back-substitute and verify.
- Choose an efficient algebraic method.
Concept lesson
Scale a whole equation
Multiplying an equation by k multiplies every term on both sides, including the constant.
Elimination workflow
Choose a variable, create equal or opposite coefficients, add opposite coefficients or subtract equal coefficients, solve, back-substitute and verify.
Create opposite coefficients
For 2x+y=8 and 3x-y=7, y coefficients are already opposite; no scaling is needed.
Eliminate and complete
Add the equations: 5x=15, so x=3. Substitute into 2x+y=8 to get y=2. Verify 3(3)-2=7.
Choose add or subtract
Solve 3x-y=15 and 2x-y=5. Since y coefficients are equal, subtract the full second equation from the first, then back-substitute and check.
Select the suitable method
Prefer substitution when a variable is already isolated or has coefficient 1; prefer elimination when coefficients already match or have a small LCM. Explain the choice before solving.
Two-mark elimination structure
Show any scaling, align like terms, display the addition or subtraction, find both values and state the ordered pair.
Exit ticket
Choose a suitable method for 2x+3y=13 and 4x-y=5, solve it, and verify the ordered pair.