Determine the solution of the system of equations represented by the lines in the graph. Check your solution by substituting into both equations. \[ \begin{array}{r}4 x-4 y=4 \\ x+y=5\end{array} \]

To solve the system of equations: \[ \begin{cases} 4x - 4y = 4 \\ x + y = 5 \end{cases} \] **Step 1: Simplify the First Equation** Divide the first equation by 4 to simplify: \[ \frac{4x - 4y}{4} = \frac{4}{4} \implies x - y = 1 \quad \text{(Equation 1)} \] **Step 2: Set Up the System** Now, the system of equations is: \[ \begin{cases} x - y = 1 \quad \text{(Equation 1)} \\ x + y = 5 \quad \text{(Equation 2)} \end{cases} \] **Step 3: Add the Equations** Add Equation 1 and Equation 2 to eliminate \( y \): \[ (x - y) + (x + y) = 1 + 5 \\ 2x = 6 \\ x = 3 \] **Step 4: Solve for \( y \)** Substitute \( x = 3 \) into Equation 2: \[ 3 + y = 5 \\ y = 5 - 3 \\ y = 2 \] **Solution:** \[ x = 3, \quad y = 2 \] **Step 5: Verify the Solution** - **First Equation:** \[ 4x - 4y = 4 \\ 4(3) - 4(2) = 12 - 8 = 4 \quad \text{✓} \] - **Second Equation:** \[ x + y = 5 \\ 3 + 2 = 5 \quad \text{✓} \] Both equations are satisfied with \( x = 3 \) and \( y = 2 \). **Final Answer:** \[ x = 3 \quad \text{and} \quad y = 2 \]