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Which of the graphs with no solution correctly shows the system of equations y=3x+4

and −3x+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 negative 1 comma 3 right parenthesis and left parenthesis 1 comma negative 3 right parenthesis. The dashed lines pass through left parenthesis 0 comma 8 right parenthesis and left parenthesis 4 comma negative 4 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 1 comma 3 right parenthesis and left parenthesis 1 comma negative 3 right parenthesis. The dashed lines pass through left parenthesis 0 comma 8 right parenthesis and left parenthesis 4 comma negative 4 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 3 comma negative 5 right parenthesis. The dashed lines pass through left parenthesis 0 comma 8 right parenthesis and left parenthesis negative 4 comma negative 4 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 3 comma negative 5 right parenthesis. The dashed lines pass through left parenthesis 0 comma 8 right parenthesis and left parenthesis negative 4 comma negative 4 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 2 right parenthesis and left parenthesis 0 comma negative 4 right parenthesis. The dashed lines pass through left parenthesis 3 comma 1 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 2 right parenthesis and left parenthesis 0 comma negative 4 right parenthesis. The dashed lines pass through left parenthesis 3 comma 1 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 2 comma negative 2 right parenthesis. The dashed lines pass through left parenthesis 0 comma 8 right parenthesis and left parenthesis 4 comma negative 4 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 2 comma negative 2 right parenthesis. The dashed lines pass through left parenthesis 0 comma 8 right parenthesis and left parenthesis 4 comma negative 4 right parenthesis.
Remaining Attempts : 3
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1 answer

To determine which graph correctly represents the system of equations with no solution, we first need to analyze the given equations:

  1. The first equation is \(y = 3x + 4\).
  2. The second equation is \(-3x + y = 8\), which can be rewritten as \(y = 3x + 8\).

Both lines have the same slope of 3, which means they are parallel. Since parallel lines do not intersect, there will be no solution for this system of equations.

Now let's analyze the provided options:

  1. First Option: The solid line (showing a slope of 3 and passing through \((-1, 3)\) and \((1, -3)\)) does not appear to have the same slope as the dashed line that passes through \((0, 8)\) and \((4, -4)\). This option does not show parallel lines.

  2. Second Option: The solid line starts at \(0, 4\) and ends with a slope that matches that of the dashed line starting at \(0, 8\) and going parallel towards negative. The solid line must represent \(y = 3x + 4\) and the dashed one \(y = 3x + 8\).

  3. Third Option: Similar analysis can be carried out, but it appears non-parallel since there's a change in slope in the lines shown.

  4. Fourth Option: The same representation as above, with slopes not matching.

Considering the analysis, the second option with the lines \(y = 3x + 4\) and \(y = 3x + 8\) represents parallel lines, indicating that there is no solution. Therefore, the second option is the correct graph that demonstrates the system of equations with no solution.