Complete the sentences below by dragging and dropping the correct coordinate pairs into the boxes. The graphs of \( 2 x+y=-1 \) and \( -x+y=5 \) intersect at the point The solution for the system of linear equations containing \( 6 x+y=19 \) and \( x+5 y=8 \) is

Let's solve each system of equations to find the required points. --- ### 1. Intersection of \( 2x + y = -1 \) and \( -x + y = 5 \) **Step 1:** Solve the system of equations. \[ \begin{cases} 2x + y = -1 \\ -x + y = 5 \end{cases} \] **Step 2:** Subtract the second equation from the first to eliminate \( y \). \[ (2x + y) - (-x + y) = -1 - 5 \\ 2x + y + x - y = -6 \\ 3x = -6 \\ x = -2 \] **Step 3:** Substitute \( x = -2 \) into one of the original equations to find \( y \). Using \( -x + y = 5 \): \[ -(-2) + y = 5 \\ 2 + y = 5 \\ y = 3 \] **Intersection Point:** \( (-2, 3) \) --- ### 2. Solution to the System \( 6x + y = 19 \) and \( x + 5y = 8 \) **Step 1:** Express \( y \) from the first equation. \[ 6x + y = 19 \\ y = 19 - 6x \] **Step 2:** Substitute \( y = 19 - 6x \) into the second equation. \[ x + 5(19 - 6x) = 8 \\ x + 95 - 30x = 8 \\ -29x + 95 = 8 \\ -29x = -87 \\ x = 3 \] **Step 3:** Substitute \( x = 3 \) back into \( y = 19 - 6x \) to find \( y \). \[ y = 19 - 6(3) \\ y = 19 - 18 \\ y = 1 \] **Solution:** \( (3, 1) \) --- **Final Answers:** 1. The graphs intersect at the point **\((-2, 3)\)**. 2. The solution for the system is **\((3, 1)\)**.