Question

Choose the correct graph of the system of inequalities:y ≥ 5x - 4y < -2x + 3

Answer 1

Given:

The inequalities are,

`\begin{gathered} y\ge5x-4 \\ y<-2x+3 \end{gathered}`

To find:

The correct graphs.

Step-by-step explanation:

Let us find the intercepts.

For the first inequality,

When x = 0, we get,

`\begin{gathered} y=0-4 \\ y=-4 \end{gathered}`

When y = 0, we get

`\begin{gathered} 0=5x-4 \\ 5x=4 \\ x=0.8 \end{gathered}`

So, the intercepts are

`(0.8,0),(0,-4)`

For the second inequality,

When x = 0, we get,

`\begin{gathered} y=0+3 \\ y=3 \end{gathered}`

When y = 0, we get

`\begin{gathered} 0=-2x+3 \\ -2x=-3 \\ x=1.5 \end{gathered}`

So, the intercepts are

`(1.5,0),(0,3)`

So, the graph becomes,