\( 3 x+2 y=7 \) and \( -3 x+y=-1 \)

Solve the system of equations \( 3x+2y=7;-3x+y=-1 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}3x+2y=7\\-3x+y=-1\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}3x+2y=7\\y=-1+3x\end{array}\right.\) - step2: Substitute the value of \(y:\) \(3x+2\left(-1+3x\right)=7\) - step3: Simplify: \(9x-2=7\) - step4: Move the constant to the right side: \(9x=7+2\) - step5: Add the numbers: \(9x=9\) - step6: Divide both sides: \(\frac{9x}{9}=\frac{9}{9}\) - step7: Divide the numbers: \(x=1\) - step8: Substitute the value of \(x:\) \(y=-1+3\times 1\) - step9: Substitute back: \(y=-1+3\) - step10: Calculate: \(y=2\) - step11: Calculate: \(\left\{ \begin{array}{l}x=1\\y=2\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=1\\y=2\end{array}\right.\) - step13: Rewrite: \(\left(x,y\right) = \left(1,2\right)\) The solution to the system of equations \(3x+2y=7\) and \(-3x+y=-1\) is \(x=1\) and \(y=2\).