Question

Please heelp me.... thanks

Answer 1

The system of linear inequalities for the given graph is
`\(y \geq (1)/(4)x + 3\)` and
`\(y \leq -2x + 3\)`, representing the shaded region where the lines intersect at (0,3).

Let's denote the variables as x and y. Based on the given points and the intersection at (0,3), we can create a system of linear inequalities:

1. The line passing through (0,3) and (4,4):

`\[ y \geq (1)/(4)x + 3 \]`

2. The line passing through (0,3) and (1,1):

`\[ y \leq -2x + 3 \]`

So, the system of linear inequalities is:

`\[ \begin{cases} y \geq (1)/(4)x + 3 \\ y \leq -2x + 3 \end{cases} \]`