Answer:
The correct option is c.
Step-by-step explanation:
The given equations are
[tex]x-y-z=0[/tex] .... (1)
[tex]2x-y+2z=1[/tex] ..... (2)
[tex]x-y+z=-2[/tex] .... (3)
Subtract equation (3) form equation (1).
[tex]-2z=2[/tex]
[tex]z=-1[/tex]
The value of z is -1. Put this value in equation (1) and (2).
[tex]x-y-(-1)=0[/tex]
[tex]x-y=-1[/tex] .... (4)
[tex]2x-y+2(-1)=1[/tex]
[tex]2x-y=3[/tex] ..... (5)
Subtract equation (5) from equation (4).
[tex]x=4[/tex]
[tex]y=5[/tex]
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.
