\( \begin{array}{l}x-2 y=3 \\ 5 x+3 y=2\end{array} \) The lines whose equations are shown intersect at which point? \( (1,-1) \) \( (0,312) \) \( (-1,1) \)

Solve the system of equations \( x-2y=3;5x+3y=2 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x-2y=3\\5x+3y=2\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=3+2y\\5x+3y=2\end{array}\right.\) - step2: Substitute the value of \(x:\) \(5\left(3+2y\right)+3y=2\) - step3: Simplify: \(15+13y=2\) - step4: Move the constant to the right side: \(13y=2-15\) - step5: Subtract the numbers: \(13y=-13\) - step6: Divide both sides: \(\frac{13y}{13}=\frac{-13}{13}\) - step7: Divide the numbers: \(y=-1\) - step8: Substitute the value of \(y:\) \(x=3+2\left(-1\right)\) - step9: Substitute back: \(x=3-2\) - step10: Calculate: \(x=1\) - step11: Calculate: \(\left\{ \begin{array}{l}x=1\\y=-1\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=1\\y=-1\end{array}\right.\) - step13: Rewrite: \(\left(x,y\right) = \left(1,-1\right)\) The lines whose equations are \(x-2y=3\) and \(5x+3y=2\) intersect at the point \((1,-1)\).