Question:
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 :
Correct Option: , 2
Solution:
$\mathrm{P}_{1} \equiv \mathrm{x}-4 \mathrm{y}+7 \mathrm{z}-\mathrm{g}=0$
$\mathrm{P}_{2} \equiv 3 \mathrm{x}-5 \mathrm{y}-\mathrm{h}=0$
$\mathrm{P}_{3} \equiv-2 \mathrm{x}+5 \mathrm{y}-9 \mathrm{z}-\mathrm{k}=0$
Here $\Delta=0$
$2 \mathrm{P}_{1}+\mathrm{P}_{2}+\mathrm{P}_{3}=0$ when $2 \mathrm{~g}+\mathrm{h}+\mathrm{k}=0$
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