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Question Number 100597 by bobhans last updated on 27/Jun/20

Commented by Dwaipayan Shikari last updated on 27/Jun/20

$$x+2\mid y\mid =3$$$$Firstcasex+2y=3$$$$x-3y=5\Rightarrow 5y=-2\Rightarrow y=-\frac{2}{5}x=\frac{19}{5}$$$$x-y=\frac{21}{5}\{\begin{array}{l}x=\frac{19}{5}\\ y=-\frac{2}{5}\end{array}$$$$Secondcase$$$$x-2y=3andx-3y=5\Rightarrow y=-2andx=-1$$$$sox-y=1\{\begin{array}{l}x=-1\\ y=-2\end{array}$$

Answered by mathmax by abdo last updated on 27/Jun/20

$$\{\begin{array}{l}\mathrm{x}+2\mid \mathrm{y}\mid =3\\ \mathrm{x}-3\mathrm{y}=5\Rightarrow 2\mid \mathrm{y}\mid +3\mathrm{y}=-2\mathrm{and}\mathrm{x}=5+3\mathrm{y}\end{array}$$$$\mathrm{case}1\mathrm{y}⩾0\Rightarrow 5\mathrm{y}=-2\Rightarrow \mathrm{y}=-\frac{2}{5}\Rightarrow \mathrm{x}=5-\frac{6}{5}=-\frac{19}{5}\mathrm{so}$$$$\mathrm{x}-\mathrm{y}=-\frac{19}{5}+\frac{2}{5}=-\frac{17}{5}$$$$\mathrm{case}2\mathrm{y}⩽0\Rightarrow \mathrm{y}=-2\Rightarrow \mathrm{x}=5-6=-1\mathrm{so}\mathrm{x}-\mathrm{y}=-1+2=1$$

Commented by Rasheed.Sindhi last updated on 27/Jun/20

$$\mathrm{I}\mathrm{think}\mathrm{sir}\mathrm{that}:$$$$\mathrm{In}\mathrm{case}1\mathrm{if}\mathrm{y}⩾0\mathrm{then}\mathrm{y}=-\frac{2}{5}\mathrm{is}$$$$\mathrm{discardable}\mathrm{and}\mathrm{for}\mathrm{that}\mathrm{x}=-\frac{19}{5}$$$$\mathrm{is}\mathrm{also}\mathrm{discardable}.$$

Answered by john santu last updated on 27/Jun/20

$$\mid \mathrm{y}\mid =\frac{3-x}{2}\Rightarrow \mathrm{y}=\pm \left(\frac{3-x}{2}\right)$$$$y=\frac{x-5}{3}\Rightarrow \pm \left(\frac{3-x}{2}\right)=\frac{x-5}{3}$$$$\pm (9-3x)=2x-10$$$$\{\begin{array}{l}9-3x=2x-10;x=\frac{19}{5}\\ 3\mathrm{x}-9=2\mathrm{x}-10;\mathrm{x}=-1\end{array}$$$$\{\begin{array}{l}\mathrm{y}=\frac{\frac{19}{5}-5}{3}=\frac{-2}{5}\\ \mathrm{y}=\frac{-6}{2}=-2\end{array}$$$$$$

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