Question

Question

Which graph shows the solution of −3x−y=3 and y=−3x+4?(1 point)
Responses

Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.
Image with alt text: Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.

Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.

Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.

Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.
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A B C or D

Answer 1

To determine which graph represents the solution to the equations \(-3x - y = 3\) and \(y = -3x + 4\), we need to analyze the two equations.

1. Convert the first equation to slope-intercept form (y = mx + b):

   Starting with \(-3x - y = 3\): \[ -y = 3 + 3x \] \[ y = -3x - 3 \]

   So, the first equation can be expressed as \(y = -3x - 3\), which is a line with a slope of \(-3\) and a y-intercept of \(-3\).

2. The second equation is already in slope-intercept form: \[ y = -3x + 4 \] This is a line with a slope of \(-3\) and a y-intercept of \(4\).

3. Analyze the two lines:

   • Both lines have the same slope of \(-3\).
   • The first line has a y-intercept of \(-3\) and the second line has a y-intercept of \(4\).

Since both lines have the same slope but different y-intercepts, they are parallel and will never intersect.

Conclusion: The correct response is the one that depicts two parallel lines. If you describe each of the options as you have shown, please select the option that states "Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid." This describes the scenario correctly.

Answer 2

ABC or D ????

Answer 3

Based on the provided information about the equations having the same slope and different y-intercepts (indicating they are parallel lines), the correct answer would correspond to the option that describes:

Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.

Without seeing the options directly, I can't identify which one of A, B, C, or D corresponds to that description. However, based on your description:

• If one of the options states that the graph consists of two parallel lines, that would be the correct choice.

Please select that option. If you can provide more details about A, B, C, or D, I can help you make a specific identification!