Solve each system of equations by ELIMINATION. Clearly identify your solution. \( \begin{array}{ll}\text { 7. }\left\{\begin{array}{l}x-y=-10 \\ x-6 y=-25\end{array}\right. & \text { 8. } \\ 2 x+2 y=28 \\ 8 x-2 y=22\end{array} \)

Sure! Let's solve each system of equations using the **Elimination Method** and clearly identify the solutions. --- ### **Problem 7** **System of Equations:** \[ \begin{cases} x - y = -10 \quad \text{(1)} \\ x - 6y = -25 \quad \text{(2)} \end{cases} \] **Step 1: Subtract Equation (1) from Equation (2) to eliminate \( x \).** \[ \begin{align*} (x - 6y) - (x - y) &= -25 - (-10) \\ x - 6y - x + y &= -25 + 10 \\ -5y &= -15 \end{align*} \] **Step 2: Solve for \( y \).** \[ \begin{align*} -5y &= -15 \\ y &= \frac{-15}{-5} \\ y &= 3 \end{align*} \] **Step 3: Substitute \( y = 3 \) into Equation (1) to solve for \( x \).** \[ \begin{align*} x - y &= -10 \\ x - 3 &= -10 \\ x &= -10 + 3 \\ x &= -7 \end{align*} \] **Solution:** \[ x = -7, \quad y = 3 \] --- ### **Problem 8** **System of Equations:** \[ \begin{cases} 2x + 2y = 28 \quad \text{(1)} \\ 8x - 2y = 22 \quad \text{(2)} \end{cases} \] **Step 1: Add Equation (1) and Equation (2) to eliminate \( y \).** \[ \begin{align*} (2x + 2y) + (8x - 2y) &= 28 + 22 \\ 2x + 2y + 8x - 2y &= 50 \\ 10x &= 50 \end{align*} \] **Step 2: Solve for \( x \).** \[ \begin{align*} 10x &= 50 \\ x &= \frac{50}{10} \\ x &= 5 \end{align*} \] **Step 3: Substitute \( x = 5 \) into Equation (1) to solve for \( y \).** \[ \begin{align*} 2x + 2y &= 28 \\ 2(5) + 2y &= 28 \\ 10 + 2y &= 28 \\ 2y &= 28 - 10 \\ 2y &= 18 \\ y &= \frac{18}{2} \\ y &= 9 \end{align*} \] **Solution:** \[ x = 5, \quad y = 9 \] --- **Final Answers:** - **Problem 7:** \( x = -7 \), \( y = 3 \) - **Problem 8:** \( x = 5 \), \( y = 9 \)