\( 3 x+4 y=-24 \) and \( 7 x-4 y=-16 \)

Solve the system of equations \( 3x+4y=-24;7x-4y=-16 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}3x+4y=-24\\7x-4y=-16\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=-\frac{24+4y}{3}\\7x-4y=-16\end{array}\right.\) - step2: Substitute the value of \(x:\) \(7\left(-\frac{24+4y}{3}\right)-4y=-16\) - step3: Multiply the terms: \(-\frac{7\left(24+4y\right)}{3}-4y=-16\) - step4: Multiply both sides of the equation by LCD: \(\left(-\frac{7\left(24+4y\right)}{3}-4y\right)\times 3=-16\times 3\) - step5: Simplify the equation: \(-168-40y=-48\) - step6: Move the constant to the right side: \(-40y=-48+168\) - step7: Add the numbers: \(-40y=120\) - step8: Change the signs: \(40y=-120\) - step9: Divide both sides: \(\frac{40y}{40}=\frac{-120}{40}\) - step10: Divide the numbers: \(y=-3\) - step11: Substitute the value of \(y:\) \(x=-\frac{24+4\left(-3\right)}{3}\) - step12: Substitute back: \(x=\frac{-24+4\times 3}{3}\) - step13: Calculate: \(x=-4\) - step14: Calculate: \(\left\{ \begin{array}{l}x=-4\\y=-3\end{array}\right.\) - step15: Check the solution: \(\left\{ \begin{array}{l}x=-4\\y=-3\end{array}\right.\) - step16: Rewrite: \(\left(x,y\right) = \left(-4,-3\right)\) The solution to the system of equations \(3x+4y=-24\) and \(7x-4y=-16\) is \(x=-4\) and \(y=-3\).