Given following system of equations \[ \begin{array}{l} x-3 y=3 \\ x+5 y=11\end{array} \] What is the value of \( x-y \) ?

Solve the system of equations \( x-3y=3;x+5y=11 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x-3y=3\\x+5y=11\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=3+3y\\x+5y=11\end{array}\right.\) - step2: Substitute the value of \(x:\) \(3+3y+5y=11\) - step3: Add the terms: \(3+8y=11\) - step4: Move the constant to the right side: \(8y=11-3\) - step5: Subtract the numbers: \(8y=8\) - step6: Divide both sides: \(\frac{8y}{8}=\frac{8}{8}\) - step7: Divide the numbers: \(y=1\) - step8: Substitute the value of \(y:\) \(x=3+3\times 1\) - step9: Simplify: \(x=6\) - step10: Calculate: \(\left\{ \begin{array}{l}x=6\\y=1\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=6\\y=1\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(6,1\right)\) The solution to the system of equations is \( x = 6 \) and \( y = 1 \). Now, we can find the value of \( x - y \) by substituting the values of \( x \) and \( y \) into the expression: \( x - y = 6 - 1 = 5 \) Therefore, the value of \( x - y \) is 5.