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 lines for the system of equations x+y=2 and −x+y=7 should be parallel.
Which of these graphs shows that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions?
None of the provided graphs show that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions.
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.
To determine whether the lines represented by the system of equations x+y=2 and −x+y=7 should be parallel or intersect, we need to analyze the equations and their graphs.
The first equation, x+y=2, is in standard form. To convert it to slope-intercept form (y = mx + b), we isolate y by subtracting x from both sides: y = -x + 2. From this form, we can determine that the slope of the line is -1 and the y-intercept is 2.
The second equation, −x+y=7, can also be converted to slope-intercept form. By isolating y, we add x to both sides: y = x + 7. Here, the slope of the line is 1, and the y-intercept is 7.
Now, let's proceed to analyze the graphs:
If the two lines intersect at a single point, it means that the system of equations has a unique solution. In this case, the lines should not be parallel.
If the two lines are parallel, they have the same slope (i.e., the coefficients of x in both equations are equal) but different y-intercepts.
Examining the slopes of the two lines in the given equations, we see that they are different (-1 and 1). Therefore, the lines represented by x+y=2 and −x+y=7 should not be parallel. Thus, the options suggesting that the lines should be parallel are incorrect.
The correct responses are:
- "The graph of x+y=2 is incorrect. The lines should intersect."
- "The graph of −x+y=7 is incorrect. The lines should intersect."