Algebraic solution by elimination
The elimination method solves a pair by making one variable cancel when the equations are added or subtracted.
Practice This ConceptMain explanation
Teacher explanation
This method is useful when the coefficients of one variable are already equal or can be made equal by multiplying one or both equations. After elimination, only one variable remains, and we solve it first. Then we substitute back to get the second variable.
Example
For 2x + 3y = 13 and 2x - y = 5, subtracting the second from the first removes x immediately.
Simple analogy
Match, cancel, solve, and return.
Common confusion
Students often add when subtraction is needed, or subtract when addition is needed, so the intended variable does not cancel.
Exam tip
Before operating on the equations, check which variable will cancel faster and choose the sign carefully.
Answer writing and exam use
1-mark use
Write the exact meaning of algebraic solution by elimination in one clean line.
2-mark use
Define algebraic solution by elimination and add one example or condition.
3-mark use
Explain algebraic solution by elimination, show the method or example, and mention the common mistake.
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