Solve the simultaneous equation \( \begin{array}{l}7 x+2 y=33 \\ 4 x+2 y=24\end{array} \)

Solve the system of equations \( 7x+2y=33;4x+2y=24 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}7x+2y=33\\4x+2y=24\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{33-2y}{7}\\4x+2y=24\end{array}\right.\) - step2: Substitute the value of \(x:\) \(4\times \frac{33-2y}{7}+2y=24\) - step3: Simplify: \(\frac{4\left(33-2y\right)}{7}+2y=24\) - step4: Multiply both sides of the equation by LCD: \(\left(\frac{4\left(33-2y\right)}{7}+2y\right)\times 7=24\times 7\) - step5: Simplify the equation: \(132+6y=168\) - step6: Move the constant to the right side: \(6y=168-132\) - step7: Subtract the numbers: \(6y=36\) - step8: Divide both sides: \(\frac{6y}{6}=\frac{36}{6}\) - step9: Divide the numbers: \(y=6\) - step10: Substitute the value of \(y:\) \(x=\frac{33-2\times 6}{7}\) - step11: Calculate: \(x=3\) - step12: Calculate: \(\left\{ \begin{array}{l}x=3\\y=6\end{array}\right.\) - step13: Check the solution: \(\left\{ \begin{array}{l}x=3\\y=6\end{array}\right.\) - step14: Rewrite: \(\left(x,y\right) = \left(3,6\right)\) The solution to the simultaneous equation is \( x = 3 \) and \( y = 6 \).