Question

Which of the following points is a solution to the system graphed below?
solid green line passing through (-8,0) (0,2) (4,3)
dotted blue line passing through (0,-5) (2.5,0) (4,3)


(1 point)
Responses

(4, 3)
(4, 3)

(2, 4)
(2, 4)

(5, -1)
(5, -1)

(-5,1)

Answer 1

To determine which point is a solution to the system of equations represented by the two lines, we need to check if each given point lies on both lines.

1. **Solid green line**: We can see that the solid green line passes through the points (-8, 0), (0, 2), and (4, 3). Therefore, any point on this line will satisfy the equation of the solid green line.

2. **Dotted blue line**: The dotted blue line passes through the points (0, -5), (2.5, 0), and (4, 3). Therefore, any point on this line will satisfy the equation of the dotted blue line.

Now we test each provided point:

- **(4, 3)**: This point is on both the solid green line and the dotted blue line, as it lies on both lines according to the points mentioned.
- **(2, 4)**: This point does not lie on either line.
- **(5, -1)**: This point does not lie on either line.
- **(-5, 1)**: This point does not lie on either line.

The only point that is a solution to the system of equations (i.e., lies on both lines) is **(4, 3)**.