Solve {l}{x_{1}+x_{2}leq4}{6x_{1}+2x_{2}geq8}{x_{1}+5x_{2}geq4}{x_{1}geq0,x_{2}geq0}{x_{1}leq3,x_{2}leq3}

$$\left. \begin{array} { l } { x _ { 1 } + x _ { 2 } \leq 4 } \\ { 6 x _ { 1 } + 2 x _ { 2 } \geq 8 } \\ { x _ { 1 } + 5 x _ { 2 } \geq 4 } \\ { x _ { 1 } \geq 0 , x _ { 2 } \geq 0 } \\ { x _ { 1 } \leq 3 , x _ { 2 } \leq 3 } \end{array} \right.$$

Solve for x_2

$$\left\{\begin{matrix}x_{2}\in \begin{bmatrix}\frac{4-x_{1}}{5},4-x_{1}\end{bmatrix}\text{, }&x_{1}>\frac{8}{7}\text{ and }x_{1}\leq 3\\x_{2}=3\text{, }&x_{1}=\frac{1}{3}\\x_{2}\in \begin{bmatrix}4-3x_{1},3\end{bmatrix}\text{, }&x_{1}>\frac{1}{3}\text{ and }x_{1}<1\\x_{2}\in \begin{bmatrix}4-3x_{1},4-x_{1}\end{bmatrix}\text{, }&x_{1}\geq 1\text{ and }x_{1}\leq \frac{8}{7}\end{matrix}\right.$$

Solve for x_1

$$\left\{\begin{matrix}x_{1}\in \begin{bmatrix}4-5x_{2},3\end{bmatrix}\text{, }&x_{2}>\frac{1}{5}\text{ and }x_{2}<\frac{4}{7}\\x_{1}\in \begin{bmatrix}\frac{4-x_{2}}{3},3\end{bmatrix}\text{, }&x_{2}\geq \frac{4}{7}\text{ and }x_{2}<1\\x_{1}\in \begin{bmatrix}\frac{4-x_{2}}{3},4-x_{2}\end{bmatrix}\text{, }&x_{2}\geq 1\text{ and }x_{2}\leq 3\\x_{1}=3\text{, }&x_{2}=\frac{1}{5}\end{matrix}\right.$$