Step 1 :The system of equations is given as follows: \[\begin{aligned} 3 x+7 y & =-42 \\ 4 x-y & =6 \end{aligned}\]
Step 2 :First, solve the second equation for y to get \(y = 4x - 6\).
Step 3 :Substitute \(y = 4x - 6\) into the first equation to get \(3x + 7(4x - 6) = -42\), which simplifies to \(31x - 42 = -42\).
Step 4 :Solve the equation \(31x - 42 = -42\) to get \(x = 0\).
Step 5 :Substitute \(x = 0\) back into the equation \(y = 4x - 6\) to get \(y = -6\).
Step 6 :So, the solution to the system of equations is \(\boxed{(0, -6)}\).