Question

A system of equations consists of two lines with the same slope. Which of the following statements is true?

O The lines are perpendicular to each other.
O
There is not enough information to know whether the system is consistent or inconsistent.
The system is consistent.
O The system is inconsistent.

Answer 1

The system is consistent.

Explanation:

Answer 2

(b) There is not enough information to know whether the system is consistent or inconsistent.

Explanation:

Given a system of equations consists of two lines with the same slope, you want to know whether the system is consistent or inconsistent, whether the lines are perpendicular, or if there is enough information to tell.

Slope

Lines with the same slope are either parallel or coincident. If they are parallel, the system of equations is inconsistent. If they are coincident, the system of equations is consistent.

Parallel or coincident lines are not perpendicular. Perpendicular lines have opposite reciprocal slopes.

Since we cannot tell whether the lines are parallel or coincident from the given description, we have to say, "there is not enough information to know."