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Maths-

General

Easy

Question

If the system of equations x + 2y – 3z = 2, (k + 3)z = 3, (2k + 1)y + z = 2 is inconsistent, then value of k can be -

–3
–1/2
1
2

The correct answer is: –3

For the given system to be inconsistent we must have $open vertical bar table row 1 2 cell negative 3 end cell row 0 0 cell k plus 3 end cell row 0 cell 2 k plus 1 end cell 1 end table close vertical bar$ = 0
$rightwards double arrow$ – (k + 3) (2k + 1) = 0  k = –3, –1/2.
For k = –3, the second becomes 0z = 3 which is impossible.
For k = –1/2, the second equation gives z = 6/5 and the third equation gives
z = 2. A contradiction.

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