Solve the following system of equations. \[ \begin{aligned}-8 x+3 y & =7 \\ 13 x-3 y & =-17\end{aligned} \]

To solve the system of equations \[ \begin{aligned} -8x + 3y & = 7 \quad \text{(1)} \\ 13x - 3y & = -17 \quad \text{(2)} \end{aligned} \] we can add the two equations to eliminate \(y\). First, we'll rewrite the equations: 1. From equation (1), we have: \[-8x + 3y = 7\] 2. From equation (2), we have: \[13x - 3y = -17\] Now, if we add both equations (1) and (2): \[ (-8x + 3y) + (13x - 3y) = 7 + (-17) \] The \(3y\) and \(-3y\) cancel out, which simplifies to: \[ -8x + 13x = -10 \] Combining the \(x\) terms gives: \[ 5x = -10 \] Now, divide both sides by 5: \[ x = -2 \] Now that we have \(x\), we can substitute this value back into one of the original equations to find \(y\). We'll use equation (1): \[ -8(-2) + 3y = 7 \] This simplifies to: \[ 16 + 3y = 7 \] Now, isolate \(y\): \[ 3y = 7 - 16 \] \[ 3y = -9 \] \[ y = -3 \] Thus, the solution to the system of equations is: \[ (x, y) = (-2, -3) \]