Solve this system algebraically. \( \begin{array}{l}9 x+2 y=5 \\ y-2 x+3=0 \\ \\ \{(-11 / 13,17 / 13)\} \\ \{(-11 / 13,-17 / 13)\} \\ \{(11 / 13,17 / 13)\} \\ \{(11 / 13,-17 / 13)\}\end{array} \)

Solve the system of equations \( 9x+2y=5;y-2x+3=0 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}9x+2y=5\\y-2x+3=0\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}9x+2y=5\\y=2x-3\end{array}\right.\) - step2: Substitute the value of \(y:\) \(9x+2\left(2x-3\right)=5\) - step3: Simplify: \(13x-6=5\) - step4: Move the constant to the right side: \(13x=5+6\) - step5: Add the numbers: \(13x=11\) - step6: Divide both sides: \(\frac{13x}{13}=\frac{11}{13}\) - step7: Divide the numbers: \(x=\frac{11}{13}\) - step8: Substitute the value of \(x:\) \(y=2\times \frac{11}{13}-3\) - step9: Calculate: \(y=-\frac{17}{13}\) - step10: Calculate: \(\left\{ \begin{array}{l}x=\frac{11}{13}\\y=-\frac{17}{13}\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=\frac{11}{13}\\y=-\frac{17}{13}\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(\frac{11}{13},-\frac{17}{13}\right)\) The solution to the system of equations is \( (x,y) = \left(\frac{11}{13},-\frac{17}{13}\right) \) or \( (x,y) = (0.846153, -1.307692) \).