b) \( x+3 y=12 \) \( 2 x+y=9 \)

Solve the system of equations \( x+3y=12;2x+y=9 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x+3y=12\\2x+y=9\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=12-3y\\2x+y=9\end{array}\right.\) - step2: Substitute the value of \(x:\) \(2\left(12-3y\right)+y=9\) - step3: Simplify: \(24-5y=9\) - step4: Move the constant to the right side: \(-5y=9-24\) - step5: Subtract the numbers: \(-5y=-15\) - step6: Change the signs: \(5y=15\) - step7: Divide both sides: \(\frac{5y}{5}=\frac{15}{5}\) - step8: Divide the numbers: \(y=3\) - step9: Substitute the value of \(y:\) \(x=12-3\times 3\) - step10: Calculate: \(x=3\) - step11: Calculate: \(\left\{ \begin{array}{l}x=3\\y=3\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=3\\y=3\end{array}\right.\) - step13: Rewrite: \(\left(x,y\right) = \left(3,3\right)\) The solution to the system of equations \(x+3y=12\) and \(2x+y=9\) is \(x=3\) and \(y=3\).