$\begin{array}{l}x+3 y=9 \\ -x+y=2\end{array}$
Final Answer: The solution to the system of equations is \(\boxed{x = \frac{3}{4}, y = \frac{11}{4}}\)
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 \(\boxed{x = \frac{3}{4}, y = \frac{11}{4}}\)