\left\{ \begin{array} { l } { 3 x _ { 1 } + 2 x _ { 2 } - 9 \geq 0 } \\ { 2 x _ { 1 } - 3 x _ { 2 } - 8 \leq 0 } \\ { 3 x _ { 1 } - 2 x _ { 2 } + 6 \geq 0 } \\ { x _ { 2 } - 5 \leq 0 } \end{array} \right.
Solve for x_2
\left\{\begin{matrix}x_{2}\in \begin{bmatrix}\frac{9-3x_{1}}{2},\frac{3x_{1}}{2}+3\end{bmatrix}\text{, }&x_{1}\geq \frac{1}{2}\text{ and }x_{1}\leq \frac{4}{3}\\x_{2}=5\text{, }&x_{1}=\frac{23}{2}\\x_{2}\in \begin{bmatrix}\frac{2x_{1}-8}{3},5\end{bmatrix}\text{, }&x_{1}\geq \frac{43}{13}\text{ and }x_{1}<\frac{23}{2}\\x_{2}\in \begin{bmatrix}\frac{9-3x_{1}}{2},5\end{bmatrix}\text{, }&x_{1}>\frac{4}{3}\text{ and }x_{1}<\frac{43}{13}\end{matrix}\right.
Solve for x_1
\left\{\begin{matrix}x_{1}\in \begin{bmatrix}-\frac{2x_{2}}{3}+3,\frac{3x_{2}}{2}+4\end{bmatrix}\text{, }&x_{2}\geq -\frac{6}{13}\text{ and }x_{2}\leq \frac{15}{4}\\x_{1}\in \begin{bmatrix}\frac{2x_{2}}{3}-2,\frac{3x_{2}}{2}+4\end{bmatrix}\text{, }&x_{2}>\frac{15}{4}\text{ and }x_{2}\leq 5\end{matrix}\right.
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