Use the image to answer the question.%0D%0A%0D%0A%0D%0A%0D%0ADoes the graph show the system of equations x+y=2 and −x+y=7? Should the lines for the system be parallel?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AThe graph of −x+y=7 is incorrect. The lines should be parallel.%0D%0AThe graph of negative x plus y equals 7 is incorrect. The lines should be parallel.%0D%0A%0D%0AThe graph of x+y=2 is incorrect. The lines should intersect.%0D%0AThe graph of x plus y equals 2 is incorrect. The lines should intersect.%0D%0A%0D%0ABoth graphs are correct. The lines should be parallel.%0D%0ABoth graphs are correct. The lines should be parallel.%0D%0A%0D%0AThe graph of −x+y=7 is incorrect. The lines should intersect.

Question

Use the image to answer the question.%0D%0A%0D%0A%0D%0A%0D%0ADoes the graph show the system of equations x+y=2 and −x+y=7? Should the lines for the system be parallel?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AThe graph of −x+y=7 is incorrect. The lines should be parallel.%0D%0AThe graph of negative x plus y equals 7 is incorrect. The lines should be parallel.%0D%0A%0D%0AThe graph of x+y=2 is incorrect. The lines should intersect.%0D%0AThe graph of x plus y equals 2 is incorrect. The lines should intersect.%0D%0A%0D%0ABoth graphs are correct. The lines should be parallel.%0D%0ABoth graphs are correct. The lines should be parallel.%0D%0A%0D%0AThe graph of −x+y=7 is incorrect. The lines should intersect.

Answer 1

The graph does not show the system of equations x+y=2 and −x+y=7 correctly. The lines should intersect, not be parallel.

Answer 2

Based on the given image, the correct response would be:

The graph of x+y=2 is incorrect. The lines should intersect.

Answer 3

To determine if the graph shows the system of equations x + y = 2 and −x + y = 7, we need to analyze the lines and their relationship.

First, let's check the equation x + y = 2. This equation represents a straight line on the graph. By rearranging the equation, we can rewrite it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

For x + y = 2, we subtract x from both sides to isolate y:
y = 2 - x

This equation tells us that the slope is -1, and the y-intercept is 2. By plotting these values on the graph, we can draw the line for this equation.

Next, let's examine the equation −x + y = 7. Again, we rearrange this equation to put it in slope-intercept form:
y = x + 7

This equation indicates that the slope is 1, and the y-intercept is 7. We can plot these values and draw the line corresponding to this equation.

Now, look at the graph and compare the lines to their respective equations. If the graph accurately represents the system of equations, the lines should intersect at a single point. If the lines are parallel, the graph is incorrect.

So, based on the provided information, the correct answer is:

The graph of −x + y = 7 is incorrect. The lines should be parallel.