What is the value of (x+2y) from (9x-5y=42) and (3x+5y=30)?

Correct answer: (x+2y=\frac{54}{5})

The direct answer is option C: \(x+2y=\frac{54}{5}\). Add the equations \(9x-5y=42\) and \(3x+5y=30\). The \(y\)-terms cancel: \(12x=72\), so \(x=6\). Substitute this into \(3x+5y=30\): \(18+5y=30\), hence \(5y=12\) and \(y=\frac{12}{5}\). Now calculate the requested expression, not just one variable: \(x+2y=6+2\left(\frac{12}{5}\right)=\frac{30}{5}+\frac{24}{5}=\frac{54}{5}\). Option A, \(\frac{44}{5}\), is too small and does not result from the solved values. Option B, \(\frac{49}{5}\), is also incorrect. Option C matches the exact calculation. Option D, \(\frac{59}{5}\), is too large. A useful habit is to add equations when opposite coefficients, such as \(-5y\) and \(+5y\), appear; then substitute and finally evaluate the expression asked. Do not stop after finding \(x\), because the question asks for \(x+2y\).