Ask a New Question
Menu

Which of the graphs with no solution correctly shows the system of equations y=2x+4

and −2x+y=8
?(1 point)
Responses

A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 4 right parenthesis and left parenthesis negative 2 comma 0 right parenthesis. The dashed lines pass through left parenthesis 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 4 right parenthesis and left parenthesis negative 2 comma 0 right parenthesis. The dashed lines pass through left parenthesis 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.

A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 2 comma 0 right parenthesis and left parenthesis 0 comma 4 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 2 comma 0 right parenthesis and left parenthesis 0 comma 4 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.

A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis negative 2 comma 0 right parenthesis and left parenthesis 0 comma negative 4 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis negative 2 comma 0 right parenthesis and left parenthesis 0 comma negative 4 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.

A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 4 right parenthesis and left parenthesis negative 2 comma 0 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma 8 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 4 right parenthesis and left parenthesis negative 2 comma 0 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma 8 right parenthesis.
Skip to navigation

1st 2nd 3rd or 4th

1 answer

To find the correct graph that represents a system of equations with no solution for the equations \( y = 2x + 4 \) and \( -2x + y = 8 \), we need to analyze both equations.

  1. Equation 1: \( y = 2x + 4 \)

    • This is in slope-intercept form \( y = mx + b \), where the slope \( m = 2 \) and the y-intercept is \( 4 \). The line will pass through points like \( (0, 4) \) and \( (-2, 0) \).

  2. Equation 2: Rearranging \( -2x + y = 8 \) gives us: \[ y = 2x + 8 \]

    • This line also has a slope of \( 2 \) but a different y-intercept of \( 8 \). It will be parallel to the first line, intersecting the y-axis at \( (0, 8) \) and also passing through points like \( (4, 0) \).

Since both lines have the same slope and different y-intercepts, they are parallel and will never intersect. This indicates that the system of equations has no solution.

Now, we check the provided responses to identify the graph illustrating parallel lines:

  • The first graph shows a line through \( (0, 4) \) and \( (-2, 0) \), and another dashed line through \( (4, 0) \) and \( (0, -8) \). These lines are not parallel because they intersect at the origin.

  • The second graph shows a line through \( (2, 0) \) and \( (0, 4) \), and a dashed line through \( (-4, 0) \) and \( (0, -8) \). These lines are not parallel either.

  • The third graph shows a solid line through \( (-2, 0) \) and \( (0, -4) \), and a dashed line through \( (-4, 0) \) and \( (0, -8) \). Again, these lines are not parallel.

  • The fourth graph shows a solid line through \( (0, 4) \) and \( (-2, 0) \), and a dashed line through \( (-4, 0) \) and \( (0, 8) \). Here, the dashed line has the wrong y-coordinate for the second equation, indicating that it’s not parallel to the first line.

After reviewing all these, it appears that none of the options presented show parallel lines with the correct y-intercepts that depict the system of equations that has no solution. Please double-check the descriptions to ensure we didn't miss any options or solutions that accurately represent the parallel lines needed here.