Solve {l}{2x_{1}+3x_{2}geq18}{14x_{1}+8x_{2}leq112}{-2x_{1}+3x_{2}leq6}

$$\left\{ \begin{array} { l } { 2 x _ { 1 } + 3 x _ { 2 } \geq 18 } \\ { 14 x _ { 1 } + 8 x _ { 2 } \leq 112 } \\ { - 2 x _ { 1 } + 3 x _ { 2 } \leq 6 } \end{array} \right.$$

Solve for x_2

$$\left\{\begin{matrix}x_{2}\in \begin{bmatrix}-\frac{2x_{1}}{3}+6,-\frac{7x_{1}}{4}+14\end{bmatrix}\text{, }&x_{1}\geq \frac{144}{29}\text{ and }x_{1}\leq \frac{96}{13}\\x_{2}=\frac{2x_{1}}{3}+2\text{, }&x_{1}=3\\x_{2}\in \begin{bmatrix}-\frac{2x_{1}}{3}+6,\frac{2x_{1}}{3}+2\end{bmatrix}\text{, }&x_{1}>3\text{ and }x_{1}<\frac{144}{29}\end{matrix}\right.$$

Solve for x_1

$$\left\{\begin{matrix}x_{1}\in \begin{bmatrix}-\frac{3x_{2}}{2}+9,-\frac{4x_{2}}{7}+8\end{bmatrix}\text{, }&x_{2}\geq \frac{14}{13}\text{ and }x_{2}\leq 4\\x_{1}=-\frac{4x_{2}}{7}+8\text{, }&x_{2}=\frac{154}{29}\\x_{1}\in \begin{bmatrix}\frac{3x_{2}}{2}-3,-\frac{4x_{2}}{7}+8\end{bmatrix}\text{, }&x_{2}>4\text{ and }x_{2}<\frac{154}{29}\end{matrix}\right.$$