Question

Without graphing, classify the following system as independent, dependent, or inconsistent.

Answer 1

Answer:

The system is inconsistent

Step-by-step explanation:

we know that

If a system has at least one solution, it is said to be consistent .  

If a consistent system has exactly one solution, it is independent .  

If a consistent system has an infinite number of solutions, it is dependent

If a system not have solution, it is said to be inconsistent.

In this problem we have

$-21x-3y=-24$ ----> equation A

Isolate the variable y

$3y=-21x+24$

Divide by 3 both sides

$y=-7x+8$

$y=-7x+7$ ----> equation B

Compare both lines

The lines have the same slope and different y-intercept

so

The lines are parallel

The system has no solution

therefore

The system is inconsistent