Question

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

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

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

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

D) 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.

Answer 1

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

1. **First Equation**: \(-3x - y = 3\)
- To rewrite it in slope-intercept form (y = mx + b), we solve for \(y\):
\[
-y = 3 + 3x \\
y = -3x - 3
\]
- This line has a slope of \(-3\) and a y-intercept of \(-3\).

2. **Second Equation**: \(y = -3x + 4\)
- This line is already in slope-intercept form, with a slope of \(-3\) and a y-intercept of \(4\).

Both lines have the same slope (\(-3\)), indicating that they are parallel. Since they have different y-intercepts (-3 for the first line and 4 for the second line), they will never intersect.

Given this analysis, the correct answer is:

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