10. \( \left\{\begin{array}{l}6 x-3 y=12 \\ 4 x+3 y=24\end{array}\right. \)

Solve the system of equations \( 6x-3y=12;4x+3y=24 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}6x-3y=12\\4x+3y=24\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{4+y}{2}\\4x+3y=24\end{array}\right.\) - step2: Substitute the value of \(x:\) \(4\times \frac{4+y}{2}+3y=24\) - step3: Simplify: \(8+5y=24\) - step4: Move the constant to the right side: \(5y=24-8\) - step5: Subtract the numbers: \(5y=16\) - step6: Divide both sides: \(\frac{5y}{5}=\frac{16}{5}\) - step7: Divide the numbers: \(y=\frac{16}{5}\) - step8: Substitute the value of \(y:\) \(x=\frac{4+\frac{16}{5}}{2}\) - step9: Simplify: \(x=\frac{18}{5}\) - step10: Calculate: \(\left\{ \begin{array}{l}x=\frac{18}{5}\\y=\frac{16}{5}\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=\frac{18}{5}\\y=\frac{16}{5}\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(\frac{18}{5},\frac{16}{5}\right)\) The solution to the system of equations is \( (x, y) = \left(\frac{18}{5}, \frac{16}{5}\right) \) or in decimal form \( (x, y) = (3.6, 3.2) \).