$\left\{\begin{array}{l}4 x-y=8 \\ x+y=7\end{array}\right.$

Step 1 ：\(\begin{cases} 4x-y=8 \\ x+y=7 \end{cases}\)

Step 2 ：Solve for x in the second equation: \(x = 7 - y\)

Step 3 ：Substitute the expression for x into the first equation: \(4(7 - y) - y = 8\)

Step 4 ：Solve for y: \(28 - 5y = 8\)

Step 5 ：\(y = 4\)

Step 6 ：Substitute the value of y back into the expression for x: \(x = 7 - 4\)

Step 7 ：\(x = 3\)

Step 8 ：\(\boxed{x = 3, y = 4}\)