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Question Number 125021 by Ggjj last updated on 07/Dec/20

Answered by mathmax by abdo last updated on 07/Dec/20

$$\mathrm{s}\Rightarrow \{\begin{array}{l}\mid \mathrm{x}-1\mid +\mid \mathrm{y}-5\mid =1\\ \mid \mathrm{x}-1\mid -(\mathrm{y}-5)=0\mathrm{due}\mathrm{to}\mid \mathrm{x}-1\mid ⩾0\mathrm{we}\mathrm{get}\mathrm{y}⩾5\Rightarrow \end{array}$$$$\mathrm{s}\Rightarrow \{\begin{array}{l}\mid \mathrm{x}-1\mid +\mathrm{y}-5=1\\ \mid \mathrm{x}-1\mid -(\mathrm{y}-5)=0\Rightarrow 2\mid \mathrm{x}-1\mid =1\Rightarrow \mid \mathrm{x}-1\mid =\frac{1}{2}\end{array}$$$$\Rightarrow \mathrm{x}-1=\frac{1}{2}\mathrm{or}\mathrm{x}-1=-\frac{1}{2}\Rightarrow \mathrm{x}=\frac{3}{2}\mathrm{or}\mathrm{x}=\frac{1}{2}$$$$\mathrm{x}=\frac{3}{2}\Rightarrow \mathrm{y}=5+\frac{1}{2}=\frac{11}{2}\Rightarrow \mathrm{x}+\mathrm{y}=\frac{3}{2}+\frac{11}{2}=7$$$$\mathrm{x}=\frac{1}{2}\Rightarrow \mathrm{y}=5+\frac{1}{2}=\frac{11}{2}\Rightarrow \mathrm{x}+\mathrm{y}=\frac{1}{2}+\frac{11}{2}=6$$$$\mathrm{at}\mathrm{conclusion}\mathrm{x}+\mathrm{y}\mathrm{is}\mathrm{equal}\mathrm{to}7\mathrm{or}6$$

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