If (4(x+y)+3(x-y)=62) and (2(x+y)-5(x-y)=-2), what is the value of (y)?

Correct answer: \(y=\frac{43}{13}\)

Let \(s=x+y\) and \(d=x-y\). The equations become \(4s+3d=62\) and \(2s-5d=-2\). Multiplying the second equation by 2 gives \(4s-10d=-4\). Subtracting this from the first equation gives \(13d=66\), so \(d=\frac{66}{13}\). Using \(2s-5d=-2\), we get \(s=\frac{152}{13}\). Since \(y=\frac{s-d}{2}\), \(y=\frac{43}{13}\). A nearby value such as \(\frac{40}{13}\) results from not correctly using the relation between \(x+y\) and \(x-y\). Exam tip: when these expressions repeat, substitute them as new variables to simplify elimination.