Question

Which statement best describes the system of equations y = 2x - 13, 2x -y = 13
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, but they share the same y-intercept, (0, 2). Thus, the system has one solution at (0, 2).
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.
The equations have different slopes and different y-intercepts. Thus, the system has one solution at (2,-13).

Answer 1

The first statement is correct.

Reason: 2x − y = 13 rearranges to y = 2x − 13, which is identical to y = 2x − 13. Both have slope 2 and y-intercept (0, −13), so the lines coincide and the system has infinitely many solutions.