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
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 negative x plus y equals 7 is incorrect. 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 intersect.
The graph of negative x plus y equals 7 is incorrect. The lines should intersect.
The correct response is:
The graph of −x+y=7 is incorrect. The lines should be parallel.
The graph shows the system of equations x+y=2 and −x+y=7. Both equations represent lines on the graph. If the lines were parallel, they would never intersect. However, in this case, the lines intersect at a certain point. Therefore, the correct response is: "The graph of −x+y=7 is incorrect. The lines should intersect."
To determine if the lines in the system of equations are parallel or if they intersect, we can compare the slopes of the lines.
For the equation x + y = 2, we can rewrite it in slope-intercept form (y = mx + b) by isolating y:
y = -x + 2
From this equation, we can see that the slope of the line is -1.
For the equation -x + y = 7, we can rewrite it in slope-intercept form:
y = x + 7
From this equation, we can see that the slope of the line is 1.
Since the slopes of the two lines are not equal (-1 and 1), the lines should intersect. Therefore, the correct answer is:
The graph of x+y=2 is incorrect. The lines should intersect.