# If the system of linear equations $x-4y+7z=g$$3y-5z=h$$-2x+5y-9z=k$is consistent, then :Option 1)  $g+h+k=0$Option 2)    $g+h+2k=0$Option 3)  $g+2h+k=0$Option 4)  $2g+h+k=0$

Solution of a non-homogeneous system of linear equations by matrix method -

If $A$ is a singular matrix and $Adj(A).b\neq 0$, then the system of equations given by $Ax=b$ has no solution

- wherein

Consistent system of linear equation -

If the system of equations has one or more solutions

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Given that the system of linear equation.

Let

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

Here $\Delta = 0$

$2P_1 + P_2 + P_3 = 0$  when  $2g + h + k = 0$

Option 1)

$g+h+k=0$

Option 2)

$g+h+2k=0$

Option 3)

$g+2h+k=0$

Option 4)

$2g+h+k=0$

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