Solve the system by the addition method. \( \begin{array}{l}3 x-4 y=3 \\ 5 x+3 y=-24\end{array} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \{ \}. (Type an ordered pair.) B. There are infinitely many solutions.

Solve the system of equations \( 3x-4y=3;5x+3y=-24 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}3x-4y=3\\5x+3y=-24\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{3+4y}{3}\\5x+3y=-24\end{array}\right.\) - step2: Substitute the value of \(x:\) \(5\times \frac{3+4y}{3}+3y=-24\) - step3: Simplify: \(\frac{5\left(3+4y\right)}{3}+3y=-24\) - step4: Multiply both sides of the equation by LCD: \(\left(\frac{5\left(3+4y\right)}{3}+3y\right)\times 3=-24\times 3\) - step5: Simplify the equation: \(15+29y=-72\) - step6: Move the constant to the right side: \(29y=-72-15\) - step7: Subtract the numbers: \(29y=-87\) - step8: Divide both sides: \(\frac{29y}{29}=\frac{-87}{29}\) - step9: Divide the numbers: \(y=-3\) - step10: Substitute the value of \(y:\) \(x=\frac{3+4\left(-3\right)}{3}\) - step11: Calculate: \(x=-3\) - step12: Calculate: \(\left\{ \begin{array}{l}x=-3\\y=-3\end{array}\right.\) - step13: Check the solution: \(\left\{ \begin{array}{l}x=-3\\y=-3\end{array}\right.\) - step14: Rewrite: \(\left(x,y\right) = \left(-3,-3\right)\) The solution to the system of equations \(3x-4y=3\) and \(5x+3y=-24\) is \((-3,-3)\). Therefore, the correct choice is A. The solution set is \((-3,-3)\).