Answer
No solution.
Work Step by Step
The given equations are
$\Rightarrow 2x+y+2z=1$ ......(1)
$\Rightarrow 3x-y+z=2$ ......(2)
$\Rightarrow x-2y-z=0$ ......(3)
Multiply equation (1) by $2$.
$\Rightarrow 4x+2y+4z=2$ ......(4)
Now add equation (3) and (4).
$\Rightarrow x-2y-z+4x+2y+4z=0+2$
Add like terms.
$\Rightarrow 5x+3z=2$ ...... (5)
Add equation (1) and (2).
$\Rightarrow 2x+y+2z+3x-y+z=1+2$
Add like terms
$\Rightarrow 5x+3z=3$ ......(6)
Subtract equation (5) from equation (6).
$\Rightarrow 5x+3z-(5x+3z)=3-2$
Simplify.
$\Rightarrow 5x+3z-5x-3z=1$
$\Rightarrow 0=1$
The above statement is false.
Hence, there is no solution.
