\( y-3 x=-2 \) and \( 7 x-2 y=8 \)

Solve the system of equations \( y-3x=-2;7x-2y=8 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}y-3x=-2\\7x-2y=8\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}y=-2+3x\\7x-2y=8\end{array}\right.\) - step2: Substitute the value of \(y:\) \(7x-2\left(-2+3x\right)=8\) - step3: Simplify: \(x+4=8\) - step4: Move the constant to the right side: \(x=8-4\) - step5: Subtract the numbers: \(x=4\) - step6: Substitute the value of \(x:\) \(y=-2+3\times 4\) - step7: Calculate: \(y=10\) - step8: Calculate: \(\left\{ \begin{array}{l}x=4\\y=10\end{array}\right.\) - step9: Check the solution: \(\left\{ \begin{array}{l}x=4\\y=10\end{array}\right.\) - step10: Rewrite: \(\left(x,y\right) = \left(4,10\right)\) The solution to the system of equations \(y-3x=-2\) and \(7x-2y=8\) is \(x=4\) and \(y=10\).