The number of solutions of the system of equations $2 x+y-z=7, \quad x-3 y+2 z=1$, $x+4 y-3 z=5$ is
The number of solutions of the system of equations $2 x+y-z=7, \quad x-3 y+2 z=1$, $x+4 y-3 z=5$ is
0
1
2
3
Solution
Given that,
$2 x+y-z=7$ $\ldots$ (i)
$x-3 y+2 z=1$ $\ldots$ (ii)
and $x+4 y-z=5$ $\ldots$ (iii)
From Eqs. (i) and (ii),
$5 x-y=15$ $\ldots$ (iv)
From Eqs. (i) and (iii),
$5 x-y=16$ $\ldots$ (v)
Equation (iv) and (v) shows that they are parallel and solution does not exist.