Question

Does the graph show the system of equations x + y = 2 and - x + y = 7 Should the lines for the system be parallel?

The graph of - x + y = 7 is incorrect. The lines should intersect.

The graph of - x + y = 7 is incorrect. The lines should be parallel.

The graph of x + y = 2 is incorrect. The lines should intersect.

Both graphs are correct. The lines should be parallel.

Answer 1

To determine whether the lines represented by the equations \( x + y = 2 \) and \( -x + y = 7 \) should be parallel or intersect, we can analyze the equations of the lines.

1. **Convert the equations to slope-intercept form (y = mx + b)**:
- For \( x + y = 2 \):
\[
y = -x + 2
\]
The slope (m) is -1.

- For \( -x + y = 7 \):
\[
y = x + 7
\]
The slope (m) is 1.

2. **Compare the slopes**:
- The first line has a slope of -1.
- The second line has a slope of 1.

Since the slopes of the two lines are different, the lines will intersect at some point. They are not parallel.

Given this analysis, the correct statement based on the provided options is:
- The graph of \( -x + y = 7 \) is incorrect. The lines should intersect.