Answer: \( \begin{array}{l}\text { 8) Solve the system of equations } \\ 2 x+3 y=7 \\ 2 x-3 y=-5\end{array} \) Show Your Work (4 points)

To solve the system of equations: 1. Start with the original equations: \[ 2x + 3y = 7 \quad (1) \] \[ 2x - 3y = -5 \quad (2) \] 2. To eliminate \( x \), subtract Equation (2) from Equation (1): \[ (2x + 3y) - (2x - 3y) = 7 - (-5) \] This simplifies to: \[ 6y = 12 \] Thus, divide by 6: \[ y = 2 \] 3. Now that we have \( y \), substitute back into Equation (1) to solve for \( x \): \[ 2x + 3(2) = 7 \] \[ 2x + 6 = 7 \] Subtract 6 from both sides: \[ 2x = 1 \] Finally, divide by 2: \[ x = 0.5 \] 4. The solution to the system of equations is: \[ x = 0.5, \, y = 2 \] Thus, the ordered pair solution is \((0.5, 2)\).