Which statement best describes the system of equations {y=−3x+7y=−3x−7

Question

{
𝑦
=
−
3
𝑥
+
7
𝑦
=
−
3
𝑥
−
7
?(1 point)
Responses

Both equations have a slope of −3, and they share the same y-intercept. Thus, the system has an infinite number of solutions because they are identical lines.
Both equations have a slope of negative 3 , and they share the same y -intercept. Thus, the system has an infinite number of solutions because they are identical lines.

The equations have different slopes and different y-intercepts. Thus, the system has one solution at (−3,7).
The equations have different slopes and different y -intercepts. Thus, the system has one solution at left parenthesis negative 3 comma 7 right parenthesis .

The equations have different slopes, but they share the same y-intercept, (0,−3). Thus, the system has one solution at (0,−3).
The equations have different slopes, but they share the same y -intercept, left parenthesis 0 comma negative 3 right parenthesis . Thus, the system has one solution at left parenthesis 0 comma negative 3 right parenthesis .

Both equations have a slope of −3, but they do not share the same y-intercept. Thus, the system has no solutions because the lines are parallel.

Answer 1

To analyze the given system of equations:

1. The first equation is \(y = -3x + 7\).
2. The second equation is \(y = -3x - 7\).

From this, we can determine the following:

• Both equations have the same slope of \(-3\).
• The y-intercepts are different: \(7\) for the first equation and \(-7\) for the second equation.

Since the slopes are the same (both are \(-3\)) but the y-intercepts are different, this means the two lines are parallel.

Thus, the correct description is:

"Both equations have a slope of \(-3\), but they do not share the same y-intercept. Thus, the system has no solutions because the lines are parallel."