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

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

Tardigrade Admin · Accepted Answer

P1 ≡ x - 4y + 7z - g = 0 P2 ≡ 3x - 5y - h = 0 P3 ≡ -2x + 5y - 9z - k = 0 Here Δ = 0 2P1 + P2 + P3 = 0 when 2g + h + k = 0

Q. 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 :

$g + h + k = 0$

$2 g + h + k = 0$

$g + h + 2 k = 0$

$g + 2 h + k = 0$

$P_{1} \equiv x - 4 y + 7 z - g = 0$
$P_{2} \equiv 3 x - 5 y - h = 0$
$P_{3} \equiv - 2 x + 5 y - 9 z - k = 0$
Here $Δ = 0$
$2 P_{1} + P_{2} + P_{3} = 0$ when $2 g + h + k = 0$

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

g+h+k=0

2g+h+k=0

g+h+2k=0

g+2h+k=0