8) \( \begin{array}{l}7 x+2 y=24 \\ 8 x+2 y=30\end{array} \)

Solve the system of equations \( 7x+2y=24;8x+2y=30 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}7x+2y=24\\8x+2y=30\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{24-2y}{7}\\8x+2y=30\end{array}\right.\) - step2: Substitute the value of \(x:\) \(8\times \frac{24-2y}{7}+2y=30\) - step3: Simplify: \(\frac{8\left(24-2y\right)}{7}+2y=30\) - step4: Multiply both sides of the equation by LCD: \(\left(\frac{8\left(24-2y\right)}{7}+2y\right)\times 7=30\times 7\) - step5: Simplify the equation: \(192-2y=210\) - step6: Move the constant to the right side: \(-2y=210-192\) - step7: Subtract the numbers: \(-2y=18\) - step8: Change the signs: \(2y=-18\) - step9: Divide both sides: \(\frac{2y}{2}=\frac{-18}{2}\) - step10: Divide the numbers: \(y=-9\) - step11: Substitute the value of \(y:\) \(x=\frac{24-2\left(-9\right)}{7}\) - step12: Calculate: \(x=6\) - step13: Calculate: \(\left\{ \begin{array}{l}x=6\\y=-9\end{array}\right.\) - step14: Check the solution: \(\left\{ \begin{array}{l}x=6\\y=-9\end{array}\right.\) - step15: Rewrite: \(\left(x,y\right) = \left(6,-9\right)\) The solution to the system of equations is \( x = 6 \) and \( y = -9 \).