[tex]\begin{gathered} \begin{bmatrix}x\ge\: -2 \\ y>-7 \\ 5x+6y\le\: -12\end{bmatrix} \\ 5x+6y\le\: -12 \\ 5x+6y-5x\le\: -12-5x \\ 6y\le\: -12-5x \\ \frac{6y}{6}\le\: -\frac{12}{6}-\frac{5x}{6} \\ y\le\frac{-12-5x}{6} \\ \begin{bmatrix}x\ge\: -2 \\ y>-7 \\ y\le\frac{-12-5x}{6}\end{bmatrix}\text{ }finite\text{ solutions} \end{gathered}[/tex]
graphing we get
the solution to the system will be the area where the shades of each inequality intersect
