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.

To solve the system using the addition method, we first need to manipulate the equations to eliminate one variable. Start with the original equations: 1. \(3x - 4y = 3\) 2. \(5x + 3y = -24\) Let's multiply the first equation by 3 and the second equation by 4 to align coefficients for \(y\): - \(9x - 12y = 9\) (First equation multiplied by 3) - \(20x + 12y = -96\) (Second equation multiplied by 4) Now, add these two new equations: \((9x - 12y) + (20x + 12y) = 9 - 96\) This simplifies to: \(29x = -87\) Solving for \(x\): \(x = -3\) Now, substitute \(x = -3\) back into one of the original equations to find \(y\). Using the first equation: \(3(-3) - 4y = 3\) \(-9 - 4y = 3\) \(-4y = 12\) \(y = -3\) So, the solution set is \((-3, -3)\). A. The solution set is \{ (-3, -3) \}.