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Which statement best describes the system of equations {y=2x+13y=2x+1

?(1 point)
Responses

The equations have different slopes, but they share the same y-intercept, (0,2)
. Thus, the system has one solution at (0,2)
.
The equations have different slopes, but they share the same y -intercept, left parenthesis 0 comma 2 right parenthesis . Thus, the system has one solution at left parenthesis 0 comma 2 right parenthesis .

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, 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.
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)
.

1 answer

To analyze the given system of equations:

  1. First Equation: \( y = 2x + 1 \)
  2. Second Equation: \( y = 2x + 13 \)

Both equations are in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

  • Slope: Both equations have the same slope of \( 2 \).
  • Y-Intercept: The first equation has a y-intercept of \( 1 \), and the second equation has a y-intercept of \( 13 \).

Since they both have the same slope (2) but different y-intercepts (1 and 13), this means the lines are parallel. Therefore, they will never intersect, indicating that there are no solutions to the system of equations.

The correct response is:

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.