Answer: \( \begin{array}{l}\text { 8) Solve the system of equations } \\ 2 x+3 y=7 \\ 2 x-3 y=-5\end{array} \) Show Your Work (4 points)

Solve the system of equations \( 2x+3y=7;2x-3y=-5 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2x+3y=7\\2x-3y=-5\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{7-3y}{2}\\2x-3y=-5\end{array}\right.\) - step2: Substitute the value of \(x:\) \(2\times \frac{7-3y}{2}-3y=-5\) - step3: Simplify: \(7-6y=-5\) - step4: Move the constant to the right side: \(-6y=-5-7\) - step5: Subtract the numbers: \(-6y=-12\) - step6: Change the signs: \(6y=12\) - step7: Divide both sides: \(\frac{6y}{6}=\frac{12}{6}\) - step8: Divide the numbers: \(y=2\) - step9: Substitute the value of \(y:\) \(x=\frac{7-3\times 2}{2}\) - step10: Calculate: \(x=\frac{1}{2}\) - step11: Calculate: \(\left\{ \begin{array}{l}x=\frac{1}{2}\\y=2\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=\frac{1}{2}\\y=2\end{array}\right.\) - step13: Rewrite: \(\left(x,y\right) = \left(\frac{1}{2},2\right)\) The solution to the system of equations \(2x+3y=7\) and \(2x-3y=-5\) is \(x=\frac{1}{2}\) and \(y=2\), or \(x=0.5\) and \(y=2\).