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=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.
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The correct response is: The graph of x+y=2 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 intersect.
To determine if the graph shows the system of equations x+y=2 and −x+y=7, we need to analyze the lines represented by the equations.
First, let's rewrite the equations in slope-intercept form (y = mx + b):
Equation 1: x + y = 2
To rewrite this equation in slope-intercept form, we can isolate y by subtracting x from both sides:
y = -x + 2
Equation 2: -x + y = 7
To rewrite this equation in slope-intercept form, we can isolate y by adding x to both sides:
y = x + 7
Now we can compare the slopes of the two equations. The slope of a line can be determined by the coefficient of x.
In Equation 1, the coefficient of x is -1, so the slope is -1.
In Equation 2, the coefficient of x is 1, so the slope is 1.
Since the slopes are different (-1 and 1), the lines represented by these equations should intersect. Therefore, if the graph of x+y=2 is incorrect, the lines should intersect, and if the graph of −x+y=7 is incorrect, the lines should also intersect.
So, the correct response is: The graph of x+y=2 is incorrect. The lines should intersect.