c) \( x+3 y=17 \) and \( 4 x-2 y=12 \)

Solve the system of equations \( x+3y=17;4x-2y=12 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x+3y=17\\4x-2y=12\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=17-3y\\4x-2y=12\end{array}\right.\) - step2: Substitute the value of \(x:\) \(4\left(17-3y\right)-2y=12\) - step3: Simplify: \(68-14y=12\) - step4: Move the constant to the right side: \(-14y=12-68\) - step5: Subtract the numbers: \(-14y=-56\) - step6: Change the signs: \(14y=56\) - step7: Divide both sides: \(\frac{14y}{14}=\frac{56}{14}\) - step8: Divide the numbers: \(y=4\) - step9: Substitute the value of \(y:\) \(x=17-3\times 4\) - step10: Calculate: \(x=5\) - step11: Calculate: \(\left\{ \begin{array}{l}x=5\\y=4\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=5\\y=4\end{array}\right.\) - step13: Rewrite: \(\left(x,y\right) = \left(5,4\right)\) The solution to the system of equations \(x+3y=17\) and \(4x-2y=12\) is \(x=5\) and \(y=4\).