What is the solution of (2(x+y)=34) and (3(x-y)=15)?

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.