Question

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

• A. $g + h + k = 0$
• B. $2g + h + k = 0$
• C. $g + h + 2k = 0$
• D. $g + 2h + k = 0$

Answer 1

Answer: (B)

$P_1 \; \equiv \; x - 4y + 7z - g = 0$
$P_2 \; \equiv \; 3x - 5y - h = 0$
$P_3 \; \equiv \; -2x + 5y - 9z - k = 0$
Here $\Delta = 0$
$2P_1 + P_2 + P_3 = 0 $ when $2g + h + k = 0$