Solve the system by substitution: \[ \begin{array}{l}5 \mathrm{x}+4 \mathrm{y}=-14 \\ \mathrm{y}=-7 \mathrm{x}-15\end{array} \]

Solve the system of equations \( 5x+4y=-14;y=-7x-15 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}5x+4y=-14\\y=-7x-15\end{array}\right.\) - step1: Substitute the value of \(y:\) \(5x+4\left(-7x-15\right)=-14\) - step2: Simplify: \(-23x-60=-14\) - step3: Move the constant to the right side: \(-23x=-14+60\) - step4: Add the numbers: \(-23x=46\) - step5: Change the signs: \(23x=-46\) - step6: Divide both sides: \(\frac{23x}{23}=\frac{-46}{23}\) - step7: Divide the numbers: \(x=-2\) - step8: Substitute the value of \(x:\) \(y=-7\left(-2\right)-15\) - step9: Simplify: \(y=-1\) - step10: Calculate: \(\left\{ \begin{array}{l}x=-2\\y=-1\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=-2\\y=-1\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(-2,-1\right)\) The solution to the system of equations by substitution is \( x = -2 \) and \( y = -1 \).