Q58 / 90 · JEE Main 2019 (09 Jan Shift 2) · Mathematics

If the system of linear equations $x - 4 y + 7 z = g$ ; $3 y - 5 z = h$ ; $- 2 x + 5 y - 9 z = k$ is consistent, then:

A
$g + h + 2 k = 0$
B
$g + 2 h + k = 0$
Correct answer
C
$2 g + h + k = 0$
D
$g + h + k = 0$

Solution

x - 4 y + 7 z = g

...(i)

3 y - 5 z = h

...(ii)

- 2 x + 5 y - 9 z = k

...(iii)

(i) + (ii), we get

x - y + 2 z = g + h

...(iv)

(ii) - (iii), we get

2 x - 2 y + 4 z = h - k

\Rightarrow x - y + 2 z = \frac{h - k}{2}

...(v)

Since, coefficient of

x, y, z

in (iv) and (v) are same. Hence, for system to be consistent

g + h = \frac{h - k}{2}

\Rightarrow 2 g + 2 h = h - k

\Rightarrow 2 g + h + k = 0

Hence, the correct answer is option: 'C'.

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