Question

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

(-21x - 3y = -24
y = -7x+7

Answer 1

The system is inconsistent

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