Step 1 :Define the system of equations as \(2x - 7y = 2\) and \(3x + y = -20\)
Step 2 :Multiply the second equation by 7 to get \(21x + 7y = -140\)
Step 3 :Add the two equations to eliminate y, resulting in \(23x = -138\)
Step 4 :Solve for x to get \(x = -6\)
Step 5 :Substitute \(x = -6\) into the first equation to solve for y, resulting in \(y = -2\)
Step 6 :The solution to the system of equations is the ordered pair \(\boxed{(-6, -2)}\)