Which statement best describes the system of equations { ? (1 point)

Question

y = 2x − 13
2x − y = 13
Both equations have a slope of 2, but they do not share the same y-intercept. Thus, the system
has no solutions because the lines are parallel.
Both equations have a slope of 2, 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 (2, −13).
The equations have different slopes, but they share the same y-intercept, . Thus, the
system has one solution at (0,2).

Answer 1

To analyze the given system of equations:

1. The first equation is \( y = 2x - 13 \). This is in slope-intercept form \( y = mx + b \), where \( m = 2 \) (slope) and \( b = -13 \) (y-intercept).

2. The second equation is \( 2x - y = 13 \). We can rearrange this into slope-intercept form by solving for \( y \): \[ -y = -2x + 13 \] \[ y = 2x - 13 \] This shows that the second equation also has a slope of 2 and a y-intercept of -13.

Since both equations have the same slope (2) and the same y-intercept (-13), they represent the same line.

Thus, the correct statement is:

Both equations have a slope of 2, and they share the same y-intercept. Thus, the system has an infinite number of solutions because they are identical lines.