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

Question

Responses

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

Two intersecting lines are graphed across a coordinate plane.

Answer 1

To determine the solution of the equations \( -3x - y = 3 \) and \( y = -3x + 4 \), we first need to rewrite the given equation into a more recognizable form.

The first equation, \( -3x - y = 3 \), can be rearranged to find \( y \):

\[ -y = 3 + 3x \] \[ y = -3x - 3 \]

Now we have two equations to analyze:

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

Next, we note the slopes of both lines:

• The slope of Equation 1 is -3.
• The slope of Equation 2 is also -3.

Since both lines have the same slope, they are parallel. Additionally, because they have different y-intercepts (one is -3 and the other is 4), they will never intersect.

Based on this information, the correct answer is:

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