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# The number of solutions of the system of equations $2x+y-z=7,x-3y+2z=1,x+4y-3z=5$ is

$\begin{array}{1 1}(A)\;3&(B)\;2\\(C)\;1&(D)\;0\end{array}$

From the given equation we get
$\Delta=\begin{vmatrix}2& 1&-1\\1&-3&2\\1&4&-3\end{vmatrix}$
$\Rightarrow 2(9-8)-1(-3-2)-1(4+3)$
$\Rightarrow 2(1)-1(-5)-1(7)$
$\Rightarrow 2+5-7$
$\Rightarrow 0$
$\Delta_1=\begin{vmatrix}7&1&-1\\1&-3&2\\5&4&-3\end{vmatrix}$
$\Rightarrow 7(9-8)-1(-3-10)-1(4+15)$
$\Rightarrow 7(1)-1(-13)-1(19)$
$\Rightarrow 7+13-19$
$\Rightarrow 20-19$
$\Rightarrow 1\neq 0$
Hence the given system no solution.
Hence (D) is the correct answer.