Question

What combinations of pots of pansies and pots of mums are solutions of the system?

Answer 1

`\begin{gathered} \text{Given} \\ x+y\ge8 \\ 5x+2y\le30 \end{gathered}`

Solve for y in each inequality.

`\begin{gathered} x+y\geq8 \\ x-x+y\ge8-x \\ \cancel{x-x}+y\ge8-x \\ y\ge8-x \end{gathered}`
`\begin{gathered} 5x+2y\le30 \\ 5x-5x+2y\le30-5x \\ \cancel{5x-5x}+2y\le30-5x \\ 2y\le30-5x \\ (2y)/(2)\le(30-5x)/(2) \\ \frac{\cancel{2}y}{\cancel{2}}\le(30-5x)/(2) \\ y\le(30-5x)/(2) \end{gathered}`

Therefore, the following are the solution

`\begin{cases}y\ge8-x \\ y\le(30-5x)/(2)\end{cases}`