Question

Which classification best describes the following system of equations?

Answer 1

Inconsistent and dependent

Answer 2

Answer:

The correct option is c.

Step-by-step explanation:

The given equations are

$x-y-z=0$                  .... (1)

$2x-y+2z=1$             ..... (2)

$x-y+z=-2$               .... (3)

Subtract equation (3) form equation (1).

$-2z=2$

$z=-1$

The value of z is -1. Put this value in equation (1) and (2).

$x-y-(-1)=0$

$x-y=-1$                .... (4)

$2x-y+2(-1)=1$

$2x-y=3$            ..... (5)

Subtract equation (5) from equation (4).

$x=4$

$y=5$

The solution of given system of equations is (4,5,-1). It is a unique solution.

Therefore the given system of equations is consistent and independent. Option c is correct.