\( 3 x+2 y=27 \) and \( y=\frac{28-2 x}{3} \)

Solve the system of equations \( 3x+2y=27;y=\frac{28-2x}{3} \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}3x+2y=27\\y=\frac{28-2x}{3}\end{array}\right.\) - step1: Substitute the value of \(y:\) \(3x+2\times \frac{28-2x}{3}=27\) - step2: Simplify: \(3x+\frac{2\left(28-2x\right)}{3}=27\) - step3: Multiply both sides of the equation by LCD: \(\left(3x+\frac{2\left(28-2x\right)}{3}\right)\times 3=27\times 3\) - step4: Simplify the equation: \(5x+56=81\) - step5: Move the constant to the right side: \(5x=81-56\) - step6: Subtract the numbers: \(5x=25\) - step7: Divide both sides: \(\frac{5x}{5}=\frac{25}{5}\) - step8: Divide the numbers: \(x=5\) - step9: Substitute the value of \(x:\) \(y=\frac{28-2\times 5}{3}\) - step10: Calculate: \(y=6\) - step11: Calculate: \(\left\{ \begin{array}{l}x=5\\y=6\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=5\\y=6\end{array}\right.\) - step13: Rewrite: \(\left(x,y\right) = \left(5,6\right)\) The solution to the system of equations is \( x = 5 \) and \( y = 6 \).