Question

PLZ help
What system of linear inequalities is shown in the graph?

Answer 1

In order find the Inequalities, First we need to Find the Equations of Both the Lines.

Equation of First line :

It is passing through the Points (0 , 2) and (4 , 0)

⇒ Slope =
`(2 - 0)/(0 - 4) = (-2)/(4) = (-1)/(2)`

⇒ Equation of the First Line :
`y - 2 = (-1)/(2)(x)`

⇒ Equation of the First Line : x + 2y = 4

Equation of Second Line :

It is passing through the Points (1.5 , 0) and (0 , -3)

⇒ Slope =
`(0 + 3)/(1.5 - 0) = (3)/(1.5) = 2`

⇒ Equation of the Second Line : y + 3 = 2x

⇒ Equation of the Second Line : 2x - y = 3

As the Shaded Area of the First Line is away from the Origin :

⇒ x + 2y ≥ 4

As the Shaded Area of the Second Line is towards the Origin and it is a Dotted line :

⇒ 2x - y < 3

So, the System of Linear Inequalities are :

⇒ x + 2y ≥ 4

⇒ 2x - y < 3