10. \( \begin{array}{l}\frac{y}{2}-\frac{x+3}{4}=\frac{3}{2} \\ \frac{y+3}{4}-\frac{x}{2}=\frac{3}{2}\end{array} \)

Solve the system of equations \( \frac{y}{2}-\frac{x+3}{4}=\frac{3}{2}; \frac{y+3}{4}-\frac{x}{2}=\frac{3}{2} \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}\frac{y}{2}-\frac{x+3}{4}=\frac{3}{2}\\\frac{y+3}{4}-\frac{x}{2}=\frac{3}{2}\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=-9+2y\\\frac{y+3}{4}-\frac{x}{2}=\frac{3}{2}\end{array}\right.\) - step2: Substitute the value of \(x:\) \(\frac{y+3}{4}-\frac{-9+2y}{2}=\frac{3}{2}\) - step3: Subtract the terms: \(\frac{y+3}{4}+\frac{9-2y}{2}=\frac{3}{2}\) - step4: Multiply both sides of the equation by LCD: \(\left(\frac{y+3}{4}+\frac{9-2y}{2}\right)\times 4=\frac{3}{2}\times 4\) - step5: Simplify the equation: \(-3y+21=6\) - step6: Move the constant to the right side: \(-3y=6-21\) - step7: Subtract the numbers: \(-3y=-15\) - step8: Change the signs: \(3y=15\) - step9: Divide both sides: \(\frac{3y}{3}=\frac{15}{3}\) - step10: Divide the numbers: \(y=5\) - step11: Substitute the value of \(y:\) \(x=-9+2\times 5\) - step12: Simplify: \(x=1\) - step13: Calculate: \(\left\{ \begin{array}{l}x=1\\y=5\end{array}\right.\) - step14: Check the solution: \(\left\{ \begin{array}{l}x=1\\y=5\end{array}\right.\) - step15: Rewrite: \(\left(x,y\right) = \left(1,5\right)\) The solution to the system of equations is \( (x, y) = (1, 5) \).