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

Infinity Learn · Accepted Answer

here,$$D=1$$−$$4703$$−$$5$$−$$25$$−$$9=1($$−$$27+25)+4(0$$−$$10)+7(0+6)$$  expanding along $$R1=$$−$$2$$−$$40+42=0The$$ system of linear equations have infinite many solutions. [   system is consistent and does not have unique solutions as $$D=0$$] ⇒    $$D1=D2=D3=0$$ Now, $$D1=0$$⇒g−$$47h3$$−$$5k5$$−$$9=0$$⇒$$g($$−$$27+25)+4($$−$$9h+5k)+7(5h$$−$$3k)=0$$⇒−$$2g$$−$$36h+20k+35h$$−$$21k=0$$⇒−$$2g$$−h−$$k=0$$⇒$$2g+h+k=0$$

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

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

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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