\( x-y=4 \) \( x+y=8 \) The \( x \)-coordinate of the solution to the system shown is 12 4

Solve the system of equations \( x-y=4;x+y=8 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x-y=4\\x+y=8\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=4+y\\x+y=8\end{array}\right.\) - step2: Substitute the value of \(x:\) \(4+y+y=8\) - step3: Add the terms: \(4+2y=8\) - step4: Move the constant to the right side: \(2y=8-4\) - step5: Subtract the numbers: \(2y=4\) - step6: Divide both sides: \(\frac{2y}{2}=\frac{4}{2}\) - step7: Divide the numbers: \(y=2\) - step8: Substitute the value of \(y:\) \(x=4+2\) - step9: Calculate: \(x=6\) - step10: Calculate: \(\left\{ \begin{array}{l}x=6\\y=2\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=6\\y=2\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(6,2\right)\) The solution to the system of equations \(x-y=4\) and \(x+y=8\) is \(x=6\) and \(y=2\). Therefore, the \(x\)-coordinate of the solution is 6, not 12 or 4.