Answer
$(0,0,0)$
Work Step by Step
$x+5z = 0$ Equation $(1)$
$5x+y = 0$ Equation $(2)$
$y-3z = 0 $ Equation $(3)$
Equation $(2)$ $-$ Equation $(3)$
$5x+y -(y-3z) = 0 $
$5x+y-y+3z = 0$
$5x+3z = 0$ Equation $(4)$
Equation$(1) \times 5 $ $ - $ Equation $(4)$
$5(x+5z)-(5x+3z)=0$
$5x+25z -5x-3z =0$
$22z = 0$
$z = 0$
Substituting $z$ value in Equation$(1)$
$x+5z = 0$
$x+5(0) = 0$
$x = 0$
Substituting $x$ value in Equation$(2)$
$5x+y = 0$
$5(0)+y = 0$
$y = 0$
$x = 0$
$y = 0$
$z = 0$
Solution $(0,0,0)$
