Question

Which graph shows the solution to the system of linear inequalities?

y>2/3x+3
y-<-1/3x+2

Answer 1

Given:

The inequalities are:

`y>(2)/(3)x+3`

`y\leq -(1)/(3)x+2`

To find:

The graph for the given system of inequities.

Solution:

We have,

`y>(2)/(3)x+3`

`y\leq -(1)/(3)x+2`

The related equations are:

`y=(2)/(3)x+3`

`y=-(1)/(3)x+2`

Table of values

x
`y=(2)/(3)x+3`
`y=-(1)/(3)x+2`

0 3 2

3 5 1

Plot the points (0,3) and (3,5) and connect them by a straight line to get the boundary line
`y=(2)/(3)x+3`.

Plot the points (0,2) and (3,1) and connect them by a straight line to get the boundary line
`y=-(1)/(3)x+2`.

In
`y>(2)/(3)x+3`, the sign of inequality is ">" it means the boundary line is a dashed line and shaded area lies above the boundary line.

`y\leq -(1)/(3)x+2`, the sign of inequality is "
`\leq`" it means the boundary line is a solid line and shaded area lies below the boundary line.

Therefore, the required graph is shown below.