6y −2xy = 4 8z − yz = 9 10x − 4xz = 8 find x+y +z = ?


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Question Number 193284 by universe last updated on 09/Jun/23

$6 y - 2 x y = 4$ $8 z - y z = 9$ $10 x - 4 x z = 8$ $f i n d x + y + z = ?$
	Answered by deleteduser1 last updated on 09/Jun/23

	$x = 3 - \frac{4}{2 y}; y = \frac{8 z - 9}{z} = 8 - \frac{9}{z}; z = \frac{10 x - 8}{4 x} = \frac{5}{2} - \frac{2}{x}$ $\Rightarrow z = \frac{5}{2} - \frac{2}{\frac{6 y - 4}{2 y}} = \frac{5}{2} - \frac{4 y}{6 y - 4} = \frac{9}{8 - y}$ $\Rightarrow \frac{15 y - 10 - 4 y}{6 y - 4} = \frac{9}{8 - y} \Rightarrow (11 y - 10) (8 - y) = 54 y - 36$ $\Rightarrow 11 y^{2} - 44 y + 44 = 0 \Rightarrow y^{2} - 4 y + 4 = 0 \Rightarrow y = 2 (t w i c e)$ $y = 2 \Rightarrow z = \frac{9}{6} = \frac{3}{2} \Rightarrow x = 2 \Rightarrow x + y + z = \frac{11}{2}$
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