The document solves several systems of linear equations. It provides the systems of equations, solves for the solution, and checks that the solution satisfies both equations. The last system solved is 2x + 3y = 12 and 2x + y = 8, with the solution given as (3, 2).

1. Which of these points are on the line y = 3x – 4 ? (3, 5) (5, 10) (-2, -10) y = 3x – 4 5 = 3(3) – 4 5 = 9 – 4 5 = 5 (3, 5) is on the line y = 3x – 4 10 = 3(5) – 4 10 = 15 – 4 10 ≠ 11 (5, 10) is not on the line y = 3x – 4 -10 = 3(-2) – 4 -10 = -6 – 4 -10 = -10 (-2, -10) is on the line

2. Solve the system of equations: y = x + 5 y = -2x + 2 Solution: (-1, 4) y = x + 5 Slope = y-int = 1 5 y = -2x + 2 Slope = y-int = -2 2

3. Solve the system of equations: y = x + 5 y = -2x + 2 Solution: (-1, 4) Check: y = x + 5 4 = -1 + 5 4 = 4 y = -2x + 2 4 = -2(-1) + 2 4 = 2 + 2 4 = 4

4. Solve the system of equations: y = 2x + 2 y = 3x + 5 Solution: (-3, -4) y = 2x + 2 Slope = y-int = 2 2 y = 3x + 5 Slope = y-int = 3 5

5. Solve the system of equations: y = 2x + 2 y = 3x + 5 Solution: (-3, -4) Check: y = 2x + 2 -4 = 2(-3) + 2 -4 = -6 + 2 -4 = -4 y = 3x + 5 -4 = 3(-3) + 5 -4 = -9 + 5 -4 = -4

6. Solve the system of equations: 2x + 3y = 12 2x + y = 8 Solution: (3, 2) 2x + 3y = 12 x 0 6 y 4 0 y-int x-int 2x + y = 8 x 0 4 y 8 0 y-int x-int

7. Solve the system of equations: 2x + 3y = 12 2x + y = 8 Solution: (3, 2) Check: 2x + 3y = 12 2(3) + 3(2) = 12 6 + 6 = 12 12 = 12 2x + y = 8 2(3) + 2 = 8 6 + 2 = 8 8 = 8