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 .

Answer 1

To analyze the system of equations:

1. \( y = 2x - 13 \)
2. \( 2x - y = 13 \)

We can rewrite the second equation in slope-intercept form (y = mx + b):

Starting with \( 2x - y = 13 \):

• Subtract \( 2x \) from both sides: \( -y = -2x + 13 \)
• Multiply everything by -1 to solve for \( y \): \( y = 2x - 13 \)

Now we see that both equations are identical:

1. \( y = 2x - 13 \)
2. \( y = 2x - 13 \)

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

Thus, the correct description of the system 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."