Question

I've been stuck on this problem for a while, just need some help working it out! Thank you for the help if u can provide

Answer 1

Given:

`\begin{gathered} y\leq(1)/(4)x+3 \\ y\ge-x+5 \end{gathered}`

For the given inequality,

`\begin{gathered} y\leq(1)/(4)x+3 \\ \text{for x=0}\Rightarrow y=3 \end{gathered}`

So, this inequality contains all the points below point (0,3). that means it contains region D and C

`\begin{gathered} y\ge-x+5 \\ \text{for x=0}\Rightarrow y=5 \end{gathered}`

This inequality contains all the points above (0,5) and it will include the region B and C.

From above discussion, region C is common in both the inequalities.

Answer: option B)