Question

Which classification best describes the following system of equations?

x-y-z=0
2x-y 2z=1
x-y z=-2

a: inconsistent and dependent
b: consistent and dependent
c: consistent and independent
d:inconsistent and independent

Answer 1

inconsistent and dependent

Answer 2

The correct option is c.

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.