Mathematics - Determinant Question with Solution | TestHub

$x-4y+7z=g$...(i)

$3y-5z=h$...(ii)

$-2x+5y-9z=k$...(iii)

(i) + (ii), we get

$x-y+2z=g+h$...(iv)

(ii) - (iii), we get

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

$\Rightarrow x-y+2z=\frac{h-k}{2}$...(v)

Since, coefficient of$x,y,z$in (iv) and (v) are same. Hence, for system to be consistent

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

$\Rightarrow 2g+2h=h-k$

$\Rightarrow 2g+h+k=0$