$\begin{array}{l}x+3 y=9 \\ -x+y=2\end{array}$

Step 1 ：Given the system of equations: \(x + 3y = 9\) and \(-x + y = 2\)

Step 2 ：Solve the second equation for y: \(y = x + 2\)

Step 3 ：Substitute \(y = x + 2\) into the first equation: \(x + 3(x + 2) = 9\)

Step 4 ：Solve for x: \(x = \frac{3}{4}\)

Step 5 ：Substitute \(x = \frac{3}{4}\) into the second equation: \(-\frac{3}{4} + y = 2\)

Step 6 ：Solve for y: \(y = \frac{11}{4}\)

Step 7 ：Final Answer: The solution to the system of equations is \(\boxed{x = \frac{3}{4}, y = \frac{11}{4}}\)