\left\{ \begin{array} { l } { y - x \leq - 2 } \\ { x + 2 y \leq 8 } \\ { 2 x - 3 y \leq 6 } \end{array} \right.
Solve for x
\left\{\begin{matrix}x\in \begin{bmatrix}y+2,8-2y\end{bmatrix}\text{, }&y\geq \frac{10}{7}\text{ and }y\leq 2\\x=\frac{3y}{2}+3\text{, }&y=-2\\x\in \begin{bmatrix}y+2,\frac{3y}{2}+3\end{bmatrix}\text{, }&y>-2\text{ and }y<\frac{10}{7}\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y\in \begin{bmatrix}\frac{2x}{3}-2,-\frac{x}{2}+4\end{bmatrix}\text{, }&x\geq 4\text{ and }x\leq \frac{36}{7}\\y\in \begin{bmatrix}\frac{2x}{3}-2,x-2\end{bmatrix}\text{, }&x\geq 0\text{ and }x<4\end{matrix}\right.
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