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Question Number 133337 by mohammad17 last updated on 21/Feb/21

Commented by Dwaipayan Shikari last updated on 21/Feb/21

$$x=3y=1z=2$$

Commented by mohammad17 last updated on 21/Feb/21

$$canyougivemestebs$$

Commented by Dwaipayan Shikari last updated on 21/Feb/21

$$x+2y+3z=11\to \left(a\right)$$$$2x-2y-z=2\to \left(b\right)$$$$a+b\Rightarrow 3x+2z=13$$$$3x-y+2z=12\to \left(c\right)\Rightarrow y=1$$$$x+3z=9\to \left(d\right)$$$$x=3,z=2$$

Commented by mohammad17 last updated on 21/Feb/21

$$pleasesirhelpme$$

Commented by bramlexs22 last updated on 21/Feb/21

$$\mathrm{this}\mathrm{not}\mathrm{triangular}\mathrm{decomposition}$$

Answered by bramlexs22 last updated on 21/Feb/21

$$\left(1\right)3\mathrm{x}-\mathrm{y}+2\mathrm{z}=12$$$$\left(2\right)\mathrm{x}+2\mathrm{y}+3\mathrm{z}=11...\times \left(3\right)$$$$\mathrm{subtract}\left(1\right)\wedge \left(2\right)$$$$\Rightarrow -7\mathrm{y}-7\mathrm{z}=-21...\left(4\right)$$$$-\mathrm{y}-\mathrm{z}=-3$$$$\left(2\right)\times 2\Rightarrow 2\mathrm{x}+4\mathrm{y}+6\mathrm{z}=22$$$$\left(3\right)\Rightarrow 2\mathrm{x}-2\mathrm{y}-\mathrm{z}=2$$$$\mathrm{subtract}\left(2\right)\wedge \left(3\right)$$$$\Rightarrow 6\mathrm{y}+7\mathrm{z}=20...\left(5\right)$$$$\left(4\right)\times 6\Rightarrow -6\mathrm{y}-6\mathrm{z}=-18$$$$\left(5\right)\Rightarrow 6\mathrm{y}+7\mathrm{z}=20$$$$\mathrm{z}=2$$$$$$$$\mathrm{then}\{\begin{array}{l}3\mathrm{x}-\mathrm{y}+2\mathrm{z}=12\\ \mathrm{y}+\mathrm{z}=3\\ \mathrm{z}=2\end{array}$$$$\mathrm{we}\mathrm{get}\{\begin{array}{l}\mathrm{y}+2=3\to \mathrm{y}=1\\ 3\mathrm{x}-1+4=12;\mathrm{x}=3\end{array}$$$$\mathrm{solution}\mathrm{set}\{3,1,2\}$$

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