Algebraic solution by substitution
The substitution method solves one equation for one variable and substitutes that expression into the other equation.
Practice This ConceptMain explanation
Teacher explanation
This method is useful when one equation already gives a variable in simple form, such as x = ... or y = .... After replacing that variable in the second equation, we get a single equation in one variable. Then we solve and back-substitute to find the other variable.
Example
If x = 2y + 1 from the first equation, put that value into the second equation to reduce the pair to one equation.
Simple analogy
First isolate, then replace.
Common confusion
Students often substitute into the same equation they used to isolate the variable, which gives no new information.
Exam tip
Choose substitution when one variable is already alone or can be made alone easily.
Answer writing and exam use
1-mark use
Write the exact meaning of algebraic solution by substitution in one clean line.
2-mark use
Define algebraic solution by substitution and add one example or condition.
3-mark use
Explain algebraic solution by substitution, show the method or example, and mention the common mistake.
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