Question

does the graph show the system of equations X Plus y equals 2 and "-1x" + y equals 7 should the lines for the system be parallel

Answer 1

To determine if the lines represented by the equations \(x + y = 2\) and \(-x + y = 7\) are parallel, we need to compare their slopes.

1. **Rewrite the equations in slope-intercept form (y = mx + b)**:

- For the first equation \(x + y = 2\):
\[
y = -x + 2
\]
Here, the slope (m) is \(-1\).

- For the second equation \(-x + y = 7\):
\[
y = x + 7
\]
Here, the slope (m) is \(1\).

2. **Compare the slopes**:
- The slope of the first line is \(-1\).
- The slope of the second line is \(1\).

Since the slopes are different (\(-1\) and \(1\)), the lines are not parallel. Instead, they will intersect at a point.

In summary, the lines represented by the equations \(x + y = 2\) and \(-x + y = 7\) are not parallel.