solve the following system of linear inequalities:
2 x + y >= 2 , x - y <= 1 , x + 2 y <= 8 , x >= 0 , y >= 0

Dear Student,

Please find below the solution to the asked query:

$$\begin{gathered} \Rightarrow 2\mathrm{x}+\mathrm{y}⩾2 , \mathrm{x}-\mathrm{y}⩽1 , \mathrm{x}+2\mathrm{y}⩽8 , \mathrm{x}⩾0 , \mathrm{y}⩾0 \\ \mathrm{So} \\ \Rightarrow 0\le \mathrm{x}\le 1 \mathrm{and} -2\left(\mathrm{x}-1\right)\le \mathrm{y}\le \frac{8-\mathrm{x}}{2} \\ \Rightarrow 1<\mathrm{x}<\frac{10}{3} \mathrm{and} \mathrm{x}-1\le \mathrm{y}\le \frac{8-\mathrm{x}}{2} \\ \Rightarrow \mathrm{x}=\frac{10}{3} \mathrm{and} \mathrm{y}=\frac{7}{3} \\ \mathrm{By} \mathrm{graph} \mathrm{also} . \end{gathered}$$




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