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=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. 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 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=2 is incorrect. The lines should intersect.
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=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. 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 intersect. The graph of negative x plus y equals 7 is incorrect. The lines should intersect.
The correct response is: Both graphs are correct. The lines should intersect.
The graph of x+y=2 is incorrect. The lines should intersect.
To determine if the lines of the system x+y=2 and −x+y=7 should be parallel or intersect, we can analyze their slopes.
For the equation x+y=2, we can rewrite it in slope-intercept form (y = mx + b) by subtracting x from both sides: y = -x + 2. From this, we can observe that the coefficient of x (the slope) is -1.
For the equation −x+y=7, we can rewrite it as y = x + 7. Again, the coefficient of x (the slope) is 1.
Since the slopes of the two equations are different, -1 and 1, the lines will intersect rather than being parallel. Therefore, the correct answer is: The graph of x+y=2 is incorrect. The lines should intersect.