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JEE MAIN 2019
09-01-19 S2
Question
If the system of linear equations $$ \begin{gathered} x-4 y+7 z=g \\ 3 y-5 z=h \\ -2 x+5 y-9 z=k \end{gathered} $$ is consistent, then
Select the correct option:
A
$g+h+k=0$
B
$g+2 h+k=0$
C
$g+h+2 k=0$
D
$2 g+h+k=0$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$$ \begin{aligned} x-4 y+7 z & =g \\ 3 y-5 z & =h \\ -2 x+5 y-9 z=k & \end{aligned} $$ from 2 (equation (i)) + equation (ii) + equation (iii): $$ \begin{aligned} & 0=2 g+h+k . \\ \therefore \quad & 2 g+h+k=0 \end{aligned} $$
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