b) \( \left\{\begin{array}{c}-3 y+4 x=-2 \\ 3 x+2 y=7\end{array}\right. \)

Solve the system of equations \( -3y+4x=-2;3x+2y=7 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}-3y+4x=-2\\3x+2y=7\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{-2+3y}{4}\\3x+2y=7\end{array}\right.\) - step2: Substitute the value of \(x:\) \(3\times \frac{-2+3y}{4}+2y=7\) - step3: Simplify: \(\frac{3\left(-2+3y\right)}{4}+2y=7\) - step4: Multiply both sides of the equation by LCD: \(\left(\frac{3\left(-2+3y\right)}{4}+2y\right)\times 4=7\times 4\) - step5: Simplify the equation: \(-6+17y=28\) - step6: Move the constant to the right side: \(17y=28+6\) - step7: Add the numbers: \(17y=34\) - step8: Divide both sides: \(\frac{17y}{17}=\frac{34}{17}\) - step9: Divide the numbers: \(y=2\) - step10: Substitute the value of \(y:\) \(x=\frac{-2+3\times 2}{4}\) - step11: Calculate: \(x=1\) - step12: Calculate: \(\left\{ \begin{array}{l}x=1\\y=2\end{array}\right.\) - step13: Check the solution: \(\left\{ \begin{array}{l}x=1\\y=2\end{array}\right.\) - step14: Rewrite: \(\left(x,y\right) = \left(1,2\right)\) La solución de las ecuaciones dadas es \( (x,y) = (1,2) \).