Solve the system of linear equations: $\left\{\begin{array}{c}-x+5 y=-6 \\ 2 x-12+y=0\end{array}\right.$

Step 1 ：Given the system of linear equations: \(\begin{cases} -x + 5y = -6 \\ 2x + y - 12 = 0 \end{cases}\)

Step 2 ：Solve the first equation for x: \(x = 5y + 6\)

Step 3 ：Substitute x in the second equation: \(2(5y + 6) + y - 12 = 0\)

Step 4 ：Simplify the equation to find y: \(11y = 0\)

Step 5 ：Solve for y: \(y = 0\)

Step 6 ：Substitute y = 0 back into the first equation to find x: \(x = 5(0) + 6 = 6\)

Step 7 ：Final Answer: The solution to the system of equations is \(\boxed{x = 6, y = 0}\)