Solve the system by the addition method. \( \begin{array}{r}3 x-4 y=-7 \\ 5 x-3 y=-8\end{array} \) Select the correct choice below and fill in any answer boxes present in your choice. A. The solution set is \( \} \). (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

To solve the system of equations using the addition method, we can first manipulate the equations to eliminate one of the variables. Starting with the equations: 1. \(3x - 4y = -7\) (Equation 1) 2. \(5x - 3y = -8\) (Equation 2) To eliminate \(y\), we can multiply Equation 1 by 3 and Equation 2 by 4 to align the coefficients of \(y\): \[ 3(3x - 4y) = 3(-7) \implies 9x - 12y = -21 \] \[ 4(5x - 3y) = 4(-8) \implies 20x - 12y = -32 \] Next, we'll subtract the first modified equation from the second: \[ (20x - 12y) - (9x - 12y) = -32 - (-21) \] This simplifies to: \[ 20x - 9x = -32 + 21 \implies 11x = -11 \] Dividing both sides by 11 gives: \[ x = -1 \] Now that we have \(x\), we can substitute \(x = -1\) into one of the original equations to find \(y\). Let's use Equation 1: \[ 3(-1) - 4y = -7 \] \[ -3 - 4y = -7 \] \[ -4y = -7 + 3 \implies -4y = -4 \] \[ y = 1 \] Thus, the solution to the system of equations is \( (-1, 1) \). This leads us to the conclusion: A. The solution set is \( (-1, 1) \).