$\begin{aligned} 4 x+y & =1 \\ x+2 y & =9\end{aligned}$

Step 1 ：We have a system of linear equations: \(4x + y = 1\) and \(x + 2y = 9\)

Step 2 ：First, we solve the first equation for y: \(y = 1 - 4x\)

Step 3 ：Then, we substitute y in the second equation with the expression we got from the first equation: \(x + 2(1 - 4x) = 9\)

Step 4 ：Solving this equation gives us the value of x: \(x = -1\)

Step 5 ：Substituting x back into the first equation gives us the value of y: \(y = 5\)

Step 6 ：The solution to the system of equations is \(\boxed{x = -1, y = 5}\)