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  4. The number of solutions of the system of equations 2x + y − z = 7 , x − 3y + 2z = 1 and x + 4y − 3z = 5 is

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Q. The number of solutions of the system of equations $ 2x + y − z = 7 $ , $ x − 3y + 2z = 1 $ and $ x + 4y − 3z = 5 $ is

UPSEEUPSEE 2012

Solution:

$\Delta=\begin{vmatrix}2 & 1 & -1 \\ 1 & -3 & 2 \\ 1 & 4 & -3\end{vmatrix}$
$=2(9-8)-1(-3-2)-1(4+3)$
$=7-7=0$
Hence, number of solutions is zero.