Use the image to answer the question.

Question

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

(1 point)
Responses

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

The graph of −x+y=7 is incorrect. The lines should be parallel.
The graph of negative x plus y equals 7 is incorrect. The lines should be parallel.

The graph of −x+y=7 is incorrect. The lines should intersect.
The graph of negative x plus y equals 7 is incorrect. The lines should intersect.

Both graphs are correct. The lines should be parallel.
Both graphs are correct. The lines should be parallel.

Answer 1

To determine if the system of equations \(x + y = 2\) and \(-x + y = 7\) is represented correctly in the graph, we can analyze the nature of the equations.

1. Equation 1: \(x + y = 2\) can be rearranged to \(y = -x + 2\). This line has a slope of -1.

2. Equation 2: \(-x + y = 7\) can be rearranged to \(y = x + 7\). This line has a slope of 1.

Since the slopes of the two lines are different (-1 for the first equation and 1 for the second), the lines will intersect at one point, rather than being parallel.

Given this analysis, the correct response should indicate that both equations are represented correctly in the graph, and that the lines should intersect.

The correct response is: The graph of x + y = 2 is incorrect. The lines should intersect. (and we can infer that likewise for \(-x + y = 7\).)