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Question Number 122081 by bobhans last updated on 14/Nov/20

$$solve\{\begin{array}{l}\mid x-1\mid +\mid y-1\mid =1\\ \mid x-1\mid -y=-5\end{array}$$

Answered by mathmax by abdo last updated on 14/Nov/20

$$\Rightarrow \{\begin{array}{l}\mid \mathrm{x}-1\mid =\mathrm{y}-5\\ \mid \mathrm{y}-1\mid +\mathrm{y}=6\mathrm{let}\mathrm{solve}\mid \mathrm{y}-1\mid +\mathrm{y}=6\mathrm{withy}⩾5\end{array}$$$$\Rightarrow \mid \mathrm{y}-1\mid +\mathrm{y}-6=0$$$$\mathrm{if}\mathrm{y}⩾1\mathrm{e}\Rightarrow \mathrm{y}-1+\mathrm{y}-6=0\Rightarrow 2\mathrm{y}-7=0\Rightarrow \mathrm{y}=\frac{7}{2}\left(\mathrm{not}\mathrm{solution}\right)$$$$\mathrm{if}\mathrm{y}⩽1\mathrm{e}\Rightarrow 1-\mathrm{y}+\mathrm{y}-6=0\Rightarrow -5=0\mathrm{impossible}\Rightarrow \mathrm{no}\mathrm{solution}\mathrm{for}\mathrm{this}$$$$\mathrm{system}$$

Answered by MJS_new last updated on 14/Nov/20

$$\mid x-1\mid -y=-5\Rightarrow y=\mid x-1\mid +5$$$$\mathrm{insert}\mathrm{in}\left(1\right)$$$$\mid x-1\mid +\mid \mid x-1\mid +5-1\mid =1$$$$\mid x-1\mid +\mid \mid x-1\mid +4\mid =1$$$$\mid x-1\mid +\mid x-1\mid +4=1$$$$2\mid x-1\mid =-3$$$$\mathrm{no}\mathrm{solution}$$

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