Question

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

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 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.

Answer 1

To determine which graph shows the solution to the equations \(-3x - y = 3\) and \(y = -3x + 4\), we should first rewrite the first equation in slope-intercept form (y = mx + b) for easier comparison.

Starting with the first equation:

\[
-3x - y = 3
\]

We can isolate \(y\):

\[
-y = 3 + 3x
\]

Multiplying both sides by -1 gives:

\[
y = -3x - 3
\]

Now we have two equations in slope-intercept form:

1. \(y = -3x - 3\)
2. \(y = -3x + 4\)

Both lines have the same slope of -3, which indicates they are parallel lines. Since they have different y-intercepts (-3 and 4), they will never intersect.

From the options you provided, the correct choice would be:

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

This indicates that they do not intersect and confirms their relationship as parallel lines.