Does that 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=2 is incorrect. the lines should intersect.
the graph of -x+y=7 is incorrect. the lines should be parallel.
Both graphs are correct. the lines should be parallel.
None of the options presented are correct. The lines for the system of equations x+y=2 and -x+y=7 should actually intersect, not be parallel.
Based on the information provided, the correct statement would be:
The graphs of the system of equations x+y=2 and -x+y=7 are incorrect. The lines should intersect, not be parallel.
The statement "Both graphs are correct. The lines should be parallel" is not accurate based on the given information.
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.
First, we can rewrite the two equations in slope-intercept form (y = mx + b) to determine their slopes and y-intercepts:
Equation 1: x + y = 2
y = -x + 2
Slope = -1
y-intercept = 2
Equation 2: -x + y = 7
y = x + 7
Slope = 1
y-intercept = 7
From the slopes, we can see that the slopes are different (-1 and 1), which means the lines are not parallel. However, to determine if they intersect, we need to compare the y-intercepts.
The y-intercepts are different, with one being 2 and the other being 7. So, the lines do not intersect because their y-intercepts are not the same.
Therefore, the correct statement is that both graphs are incorrect, and the lines should neither be parallel nor intersect.