Question

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

answers:

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

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

Answer 1

you sure

Answer 2

To determine whether the lines represented by the equations \( x + y = 2 \) and \( -x + y = 7 \) are parallel or intersecting, we first need to analyze the slopes of each line.

1. **Equation**: \( x + y = 2 \)
- Rearranged: \( y = -x + 2 \)
- Slope: -1

2. **Equation**: \( -x + y = 7 \)
- Rearranged: \( y = x + 7 \)
- Slope: 1

Since the slopes of the two lines are different (-1 and 1), the lines are not parallel and will intersect at some point.

Therefore, the correct choice based on these analyses is:

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

Answer 3

Yes, I am sure. Let's break it down step-by-step again for clarity:

1. **Equation 1**: \( x + y = 2 \)
- Rearranging to slope-intercept form (y = mx + b):
\[
y = -x + 2
\]
- Here, the slope \( m_1 = -1 \).

2. **Equation 2**: \(-x + y = 7\)
- Rearranging to slope-intercept form:
\[
y = x + 7
\]
- Here, the slope \( m_2 = 1 \).

**Comparison of Slopes**:
- The first line has a slope of -1, and the second line has a slope of 1.
- Since the slopes are different (one is negative and the other is positive), the lines are not parallel and will intersect at some point.

Thus, I confirm that the statement is correct: **The graph of -x + y = 7 is incorrect. The lines should intersect.**