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

and −3x+y=8
? Graph 1,2,3 or 4?(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 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.

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.
Remaining Attempts : 3
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1 answer

To determine which graph correctly represents the system of equations \( y = 3x + 4 \) and \( -3x + y = 8 \) with no solution, we first need to analyze the equations.

  1. The first equation \( y = 3x + 4 \) has a slope of 3 and a y-intercept at (0, 4).
  2. The second equation can be rewritten as \( y = 3x + 8 \) (by adding \( 3x \) to both sides), which also has a slope of 3 but a different y-intercept at (0, 8).

Since both lines have the same slope (3) but different y-intercepts (4 and 8), they are parallel lines. Parallel lines never intersect, which means the system of equations has no solution.

Now, we look for a graph where there are two parallel lines with the characteristics described.

From your descriptions of the graphs:

  • Graph 1: One line passes through (0, 4) and (−3, −5) (which has a slope of 3) and the other line passes through (0, 8) and (−4, −4) (also has a slope of 3). These lines are parallel.
  • Graph 2, 3, and 4: The descriptions do not indicate that the lines have the necessary parallel characteristics of having the same slope.

Thus, Graph 1 is the only one that shows a system of equations that has no solution since it displays two parallel lines correctly corresponding to \( y = 3x + 4 \) and \( y = 3x + 8 \).

Therefore, the answer is Graph 1.