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.
