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Question Number 72569 by otchereabdullai@gmail.com last updated on 30/Oct/19

$$2\mathrm{x}-\mathrm{y}+3\mathrm{z}=1$$$$4\mathrm{x}+2\mathrm{y}-\mathrm{z}=-8$$$$3\mathrm{x}+\mathrm{y}+2\mathrm{z}=-1$$

Answered by MJS last updated on 30/Oct/19

$$\left(2\right)z=4x+2y+8$$$$\left(1\right)14x+5y+23=0$$$$\left(3\right)11x+5y+17=0$$$$\left(1\right)-\left(3\right)3x+6=0\Rightarrow x=-2$$$$\left(1\right)5y-5=0\Rightarrow y=1$$$$\Rightarrow z=2$$

Commented by otchereabdullai@gmail.com last updated on 30/Oct/19

$$\mathrm{thanks}\mathrm{prof}\mathrm{mjs}$$

Answered by Tanmay chaudhury last updated on 30/Oct/19

$$△=\mid 2-13\mid$$$$\mid 42-1\mid$$$$\mid 312\mid =2(4+1)+1(8+3)+3(4-6)$$$$△=15$$$$x=\frac{1}{15}\times \mid 1-13\mid$$$$\mid -82-1\mid$$$$\mid -112\mid$$$$x=\frac{1}{15}\times \{1(4+1)+1(-16-1)+3(-8+2)\}$$$$=\frac{1}{15}\times \{5-17-18\}=-2$$$$y=\frac{1}{15}\times \mid 213\mid$$$$\mid 4-8-1\mid =2(-16-1)-1(8+3)+3(-4+24)$$$$\mid 3-12\mid =-34-11+60=15$$$$soy=\frac{15}{15}=1$$$$2x-y+3z=1$$$$2\times -2-1+3z=1$$$$3z=1+5\to z=2$$$$\mathit{x}=-2\mathit{y}=1\mathit{z}=2$$

Commented by otchereabdullai@gmail.com last updated on 30/Oct/19

$$\mathrm{thanks}\mathrm{prof}\mathrm{tanmay}$$

Answered by malwaan last updated on 30/Oct/19

$$\left(1\right)+\left(3\right)5\mathit{x}+5\mathit{z}=0$$$$\Rightarrow \mathit{x}=-\mathit{z};\mathit{z}=-\mathit{x}$$$$\left(2\right)5\mathit{x}+2\mathit{y}=-8\to \ast$$$$\left(3\right)\mathit{x}+\mathit{y}=-1$$$$\Rightarrow 2\mathit{x}+2\mathit{y}=-2$$$$(\ast )3\mathit{x}=-6\therefore \mathit{x}=-2;\mathit{z}=2$$$$;\mathit{y}=2-1=1$$

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