Question

Graph the solution to the following system of inequalities x >= - 2 y > - 7 5x + 6y <= - 12

Answer 1

`\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 \\ (6y)/(6)\le\: -(12)/(6)-(5x)/(6) \\ y\le(-12-5x)/(6) \\ \begin{bmatrix}x\ge\: -2 \\ y>-7 \\ y\le(-12-5x)/(6)\end{bmatrix}\text{ }finite\text{ solutions} \end{gathered}`

graphing we get

the solution to the system will be the area where the shades of each inequality intersect