Question

A system of two linear equations is consistent and dependent. What is true about the graph of the equations?

A.
The lines are the same.
B.
The lines are parallel, but have different intercepts.
C.
The lines intersect.
D.
The lines are perpendicular.


Please select the best answer from the choices provided

A
B
C
D

Answer 1

The best answer is " The lines are the same " ⇒ A

Explanation:

A system of two linear equations can have:

• One solution ⇒ 2 intersected lines at a point

• An infinite number of solutions ⇒ same line

• No solution ⇒ 2 parallel lines

If a system has at least one solution, it is called consistent

• If a consistent system has exactly one solution, then it is called independent. they are represented by two intersected lines at a point

• If a consistent system has an infinite number of solutions, then it is called dependent. They are represented by the same line

If a system has no solution, then it is called inconsistent. they represented by two parallel lines

Let us use these facts above to solve our question

∵ A system of two linear equations is consistent and dependent

∴ The system has an infinite number of solutions

∴ The system represented graphically by the same line

∴ The best answer is " The lines are the same "