Reducing word problems to linear equations
Reducing a word problem means converting the given statements into two linear equations in two variables.
Practice This ConceptMain explanation
Teacher explanation
In such problems, the words describe two unknown quantities and two conditions. The first task is to choose variables for the unknowns and turn the statements into equations. After that, the pair can be solved by any suitable algebraic method.
Example
If the sum of two numbers is 20 and their difference is 4, we can write x + y = 20 and x - y = 4.
Simple analogy
Words first, equations next, answer last.
Common confusion
Students sometimes choose the wrong variables or translate the same statement twice instead of forming two different equations.
Exam tip
Read the problem twice: once to choose variables and once to catch the two separate conditions.
Answer writing and exam use
1-mark use
Write the exact meaning of reducing word problems to linear equations in one clean line.
2-mark use
Define reducing word problems to linear equations and add one example or condition.
3-mark use
Explain reducing word problems to linear equations, show the method or example, and mention the common mistake.
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