If (\frac{x+y}{2}=9) and (\frac{x-y}{3}=2), what are the values of (x) and (y)?
Answer and explanation
Correct answer: \(x=12,\ y=6\)
Multiplying the first equation by 2 gives \(x+y=18\), and multiplying the second equation by 3 gives \(x-y=6\). Adding these equations gives \(2x=24\), so \(x=12\). Substituting \(x=12\) into \(x+y=18\) gives \(y=6\). In option B, \(x-y=2\), so it does not satisfy the second equation. Exam tip: For linear equations involving fractions, first clear the denominators and then use elimination.
Frequently asked questions
What is the correct answer to this question?
\(x=12,\ y=6\)
Why is this the correct answer?
Multiplying the first equation by 2 gives \(x+y=18\), and multiplying the second equation by 3 gives \(x-y=6\). Adding these equations gives \(2x=24\), so \(x=12\). Substituting \(x=12\) into \(x+y=18\) gives \(y=6\). In option B, \(x-y=2\), so it does not satisfy the second equation. Exam tip: For linear equations involving fractions, first clear the denominators and then use elimination.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
