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)
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. 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 lines for the system of equations x+y=2 and −x+y=7 should intersect.
The lines for the system should intersect.
To determine if the graph shows the system of equations x+y=2 and −x+y=7, we need to analyze the lines and their relationship.
To solve this, we can compare the slopes of the two equations:
1. First equation: x+y=2
Rewrite it in slope-intercept form: y = -x + 2
Slope of the first equation: -1
2. Second equation: −x+y=7
Rewrite it in slope-intercept form: y = x + 7
Slope of the second equation: 1
Since the slopes of the two equations are not equal, the lines representing the two equations should not be parallel.
From the given options, the correct answer is "The graph of −x+y=7 is incorrect. The lines should intersect."