Question

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

Answer 1

Answer:

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

Step-by-step 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 "