8. \( \begin{array}{l}5 x-3 y=11 \\ 2 x-y=5\end{array} \)

Solve the system of equations \( 5x-3y=11;2x-y=5 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}5x-3y=11\\2x-y=5\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}5x-3y=11\\y=-5+2x\end{array}\right.\) - step2: Substitute the value of \(y:\) \(5x-3\left(-5+2x\right)=11\) - step3: Simplify: \(-x+15=11\) - step4: Move the constant to the right side: \(-x=11-15\) - step5: Subtract the numbers: \(-x=-4\) - step6: Change the signs: \(x=4\) - step7: Substitute the value of \(x:\) \(y=-5+2\times 4\) - step8: Simplify: \(y=3\) - step9: Calculate: \(\left\{ \begin{array}{l}x=4\\y=3\end{array}\right.\) - step10: Check the solution: \(\left\{ \begin{array}{l}x=4\\y=3\end{array}\right.\) - step11: Rewrite: \(\left(x,y\right) = \left(4,3\right)\) The solution to the system of equations is \( x = 4 \) and \( y = 3 \).