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 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=7 is incorrect. The lines should be parallel.
The graph of x+y=2 and −x+y=7 should intersect, so the correct response is:
The graph of x+y=2 is incorrect. The lines should intersect.
The correct response is: The graph of −x+y=7 is incorrect. The lines should intersect.
To determine if the graph shows the system of equations x+y=2 and −x+y=7, we can analyze the given options.
Option 1: The graph of x+y=2 is incorrect. The lines should intersect.
Option 2: The graph of x plus y equals 2 is incorrect. The lines should intersect.
Option 3: The graph of −x+y=7 is incorrect. The lines should intersect.
Option 4: The graph of negative x plus y equals 7 is incorrect. The lines should intersect.
Option 5: Both graphs are correct. The lines should be parallel.
Option 6: Both graphs are correct. The lines should be parallel.
Option 7: The graph of −x+y=7 is incorrect. The lines should be parallel.
From these options, we can eliminate options 1, 2, 3, and 4 since they mention that the lines should intersect, which contradicts the information given.
Now we are left with options 5, 6, and 7, which mention that the lines should be parallel. We need to determine if this is true.
To find if the lines are parallel, we can look at the slopes of the two lines in the system.
The equation x+y=2 can be rewritten in slope-intercept form as y = -x + 2. The slope of this line is -1.
Similarly, the equation −x+y=7 can be rewritten as y = x + 7. The slope of this line is 1.
Since the slopes of the two lines are not equal (one is -1 and the other is 1), the lines are not parallel.
Thus, the correct response is option 7: The graph of −x+y=7 is incorrect. The lines should be parallel.