What is the solution of (2(x+y)=34) and (3(x-y)=15)?
Answer and explanation
Correct answer: \(x=11,\ y=6\)
Dividing the first equation by 2 gives \(x+y=17\), and dividing the second equation by 3 gives \(x-y=5\). Adding these equations gives \(2x=22\), so \(x=11\). Substituting in \(x+y=17\) gives \(y=6\). Hence, the correct solution is \(x=11,\ y=6\). In option \(x=10,\ y=7\), the sum is 17, but the difference is not 5. Exam tip: first divide by any common factor to simplify the equations before eliminating a variable.
Frequently asked questions
What is the correct answer to this question?
\(x=11,\ y=6\)
Why is this the correct answer?
Dividing the first equation by 2 gives \(x+y=17\), and dividing the second equation by 3 gives \(x-y=5\). Adding these equations gives \(2x=22\), so \(x=11\). Substituting in \(x+y=17\) gives \(y=6\). Hence, the correct solution is \(x=11,\ y=6\). In option \(x=10,\ y=7\), the sum is 17, but the difference is not 5. Exam tip: first divide by any common factor to simplify the equations before eliminating a variable.
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..
