Solve for \( x \) and \( v \) simultaneously if \( x+3 y-5=0 \) \( \begin{array}{l}2 x-6 y+2=0\end{array} \)

Solve the system of equations \( x+3y-5=0;2x-6y+2=0 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x+3y-5=0\\2x-6y+2=0\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=-3y+5\\2x-6y+2=0\end{array}\right.\) - step2: Substitute the value of \(x:\) \(2\left(-3y+5\right)-6y+2=0\) - step3: Simplify: \(-12y+12=0\) - step4: Move the constant to the right side: \(-12y=0-12\) - step5: Remove 0: \(-12y=-12\) - step6: Change the signs: \(12y=12\) - step7: Divide both sides: \(\frac{12y}{12}=\frac{12}{12}\) - step8: Divide the numbers: \(y=1\) - step9: Substitute the value of \(y:\) \(x=-3\times 1+5\) - step10: Substitute back: \(x=-3+5\) - step11: Calculate: \(x=2\) - step12: Calculate: \(\left\{ \begin{array}{l}x=2\\y=1\end{array}\right.\) - step13: Check the solution: \(\left\{ \begin{array}{l}x=2\\y=1\end{array}\right.\) - step14: Rewrite: \(\left(x,y\right) = \left(2,1\right)\) The solution to the system of equations is \( x = 2 \) and \( y = 1 \).