14. \( \begin{array}{r}5 x+2 y=-1 \\ 2 x-y=-6\end{array} \)

Solve the system of equations \( 5x+2y=-1;2x-y=-6 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}5x+2y=-1\\2x-y=-6\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}5x+2y=-1\\y=6+2x\end{array}\right.\) - step2: Substitute the value of \(y:\) \(5x+2\left(6+2x\right)=-1\) - step3: Simplify: \(9x+12=-1\) - step4: Move the constant to the right side: \(9x=-1-12\) - step5: Subtract the numbers: \(9x=-13\) - step6: Divide both sides: \(\frac{9x}{9}=\frac{-13}{9}\) - step7: Divide the numbers: \(x=-\frac{13}{9}\) - step8: Substitute the value of \(x:\) \(y=6+2\left(-\frac{13}{9}\right)\) - step9: Calculate: \(y=\frac{28}{9}\) - step10: Calculate: \(\left\{ \begin{array}{l}x=-\frac{13}{9}\\y=\frac{28}{9}\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=-\frac{13}{9}\\y=\frac{28}{9}\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(-\frac{13}{9},\frac{28}{9}\right)\) The solution to the system of equations is \( (x,y) = (-\frac{13}{9},\frac{28}{9}) \) or \( (x,y) = (-1.4,3.1) \).