Use the elimination method to solve the given system of equations. Write your answer as an ordered pair \( (x, y) \). \( \left\{\begin{array}{l}5 x-3 y=8 \\ 2 x+2 y=16\end{array}\right. \)

To solve the given system of equations using the elimination method, follow these steps: \[ \begin{cases} 5x - 3y = 8 \quad \text{(Equation 1)} \\ 2x + 2y = 16 \quad \text{(Equation 2)} \end{cases} \] **Step 1: Make the coefficients of \( y \) opposites** To eliminate \( y \), we need the coefficients of \( y \) in both equations to be opposites. - Multiply Equation 1 by **2**: \[ 2 \times (5x - 3y) = 2 \times 8 \\ 10x - 6y = 16 \quad \text{(Equation 3)} \] - Multiply Equation 2 by **3**: \[ 3 \times (2x + 2y) = 3 \times 16 \\ 6x + 6y = 48 \quad \text{(Equation 4)} \] **Step 2: Add Equations 3 and 4** \[ (10x - 6y) + (6x + 6y) = 16 + 48 \\ 16x = 64 \] **Step 3: Solve for \( x \)** \[ x = \frac{64}{16} = 4 \] **Step 4: Substitute \( x = 4 \) into one of the original equations to find \( y \)** Using Equation 2: \[ 2x + 2y = 16 \\ 2(4) + 2y = 16 \\ 8 + 2y = 16 \\ 2y = 8 \\ y = 4 \] **Solution:** The solution to the system is the ordered pair \( (4, 4) \). \(\boxed{(4,\ 4)}\)