Use the elimination method to solve the system of equations. \[ \begin{array}{l} 4 x-2 y=20 \\ 3 x+7 y=-53 \end{array} \]

Step 1 ：Multiply the first equation by 3 and the second equation by 4 to get: \(12x - 6y = 60\) and \(12x + 28y = -212\)

Step 2 ：Subtract the second equation from the first to eliminate x, resulting in: \(-34y = 272\)

Step 3 ：Divide both sides by -34 to solve for y: \(y = -8\)

Step 4 ：Substitute y = -8 into the first original equation: \(4x - 2(-8) = 20\) to get \(4x = 4\)

Step 5 ：Divide both sides by 4 to solve for x: \(x = 1\)

Step 6 ：Final Answer: The solution to the system of equations is \(\boxed{x = 1}\) and \(\boxed{y = -8}\)