Question

The given system of equations is graphed on the coordinate plane.
3x + 2y = 2 - line e
3x + 2y = 8 - line f

Which statements about the system are true? (Choose two.)

Responses
The solutions to the system are (0, 1) and (0, 4).
The solutions to the system are (0, 1) and (0, 4).
It is impossible for
to equal both
and
simultaneously; therefore, the system has no solution.
It is impossible for 3 x plus 2 y to equal both 2 and 8 simultaneously; therefore, the system has no solution.
The system is inconsistent because the lines are parallel.
The system is inconsistent because the lines are parallel.
The system is consistent because the lines are parallel.
The system is consistent because the lines are parallel.
The system has no solution because the lines are perpendicular.

Answer 1

To analyze the system of equations given by the lines:

1. **3x + 2y = 2** (line e)
2. **3x + 2y = 8** (line f)

We can observe the following:

1. Both equations have the same left side (3x + 2y) but different constants on the right side (2 and 8). This indicates that the lines are parallel because they have the same slope.

2. Since the lines are parallel and have different y-intercepts, they will never intersect. Therefore, there are no points of intersection that would satisfy both equations simultaneously.

Based on this analysis, the correct statements are:

1. **It is impossible for 3x + 2y to equal both 2 and 8 simultaneously; therefore, the system has no solution.**

2. **The system is inconsistent because the lines are parallel.**

Thus, the two true statements are:
- It is impossible for 3x + 2y to equal both 2 and 8 simultaneously; therefore, the system has no solution.
- The system is inconsistent because the lines are parallel.