\left\{ \begin{array} { c } { 2 x _ { 1 } + 3 x _ { 2 } \leq 12 } \\ { - 2 x _ { 1 } + x _ { 2 } \geq - 4 } \\ { x _ { 1 } \geq 0 } \\ { x _ { 2 } \geq 0 } \end{array} \right.
Solve for x_2
\left\{\begin{matrix}x_{2}\in \begin{bmatrix}2x_{1}-4,-\frac{2x_{1}}{3}+4\end{bmatrix}\text{, }&x_{1}\geq 2\text{ and }x_{1}\leq 3\\x_{2}\in \begin{bmatrix}0,-\frac{2x_{1}}{3}+4\end{bmatrix}\text{, }&x_{1}\geq 0\text{ and }x_{1}<2\end{matrix}\right.
Solve for x_1
\left\{\begin{matrix}x_{1}\in \begin{bmatrix}0,\frac{x_{2}}{2}+2\end{bmatrix}\text{, }&x_{2}\geq 0\text{ and }x_{2}\leq 2\\x_{1}\in \begin{bmatrix}0,-\frac{3x_{2}}{2}+6\end{bmatrix}\text{, }&x_{2}>2\text{ and }x_{2}\leq 4\end{matrix}\right.
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