[tex]\begin{gathered} \text{Given} \\ x+y\ge8 \\ 5x+2y\le30 \end{gathered}[/tex]
Solve for y in each inequality.
[tex]\begin{gathered} x+y\geq8 \\ x-x+y\ge8-x \\ \cancel{x-x}+y\ge8-x \\ y\ge8-x \end{gathered}[/tex][tex]\begin{gathered} 5x+2y\le30 \\ 5x-5x+2y\le30-5x \\ \cancel{5x-5x}+2y\le30-5x \\ 2y\le30-5x \\ \frac{2y}{2}\le\frac{30-5x}{2} \\ \frac{\cancel{2}y}{\cancel{2}}\le\frac{30-5x}{2} \\ y\le\frac{30-5x}{2} \end{gathered}[/tex]
Therefore, the following are the solution
[tex]\begin{cases}y\ge8-x \\ y\le\frac{30-5x}{2}\end{cases}[/tex]
