11. Use the elimination method by subtraction to solve for \( x \) and then \( y \). Equation \( 1 \quad 4 x-7 y=18 \) Equation \( 2 \quad-3 x-7 y=-38 \) 11a First solve for \( x \) ( \( x=8 \) 11b Now solve for \( y \) Enter your next step here

Solve the system of equations \( 4x-7y=18;-3x-7y=-38 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}4x-7y=18\\-3x-7y=-38\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{18+7y}{4}\\-3x-7y=-38\end{array}\right.\) - step2: Substitute the value of \(x:\) \(-3\times \frac{18+7y}{4}-7y=-38\) - step3: Simplify: \(-\frac{3\left(18+7y\right)}{4}-7y=-38\) - step4: Multiply both sides of the equation by LCD: \(\left(-\frac{3\left(18+7y\right)}{4}-7y\right)\times 4=-38\times 4\) - step5: Simplify the equation: \(-54-49y=-152\) - step6: Move the constant to the right side: \(-49y=-152+54\) - step7: Add the numbers: \(-49y=-98\) - step8: Change the signs: \(49y=98\) - step9: Divide both sides: \(\frac{49y}{49}=\frac{98}{49}\) - step10: Divide the numbers: \(y=2\) - step11: Substitute the value of \(y:\) \(x=\frac{18+7\times 2}{4}\) - step12: Calculate: \(x=8\) - step13: Calculate: \(\left\{ \begin{array}{l}x=8\\y=2\end{array}\right.\) - step14: Check the solution: \(\left\{ \begin{array}{l}x=8\\y=2\end{array}\right.\) - step15: Rewrite: \(\left(x,y\right) = \left(8,2\right)\) The solution to the system of equations is \( x = 8 \) and \( y = 2 \).