Question

What linear inequalitirs represnt this
please help me​

Answer 1

The system of inequalities is

`y\leq 4`

`y\geq 2x-2`

`y>-(3)/(4)x+1`

Explanation:

In this problem we have three inequalities

First inequality

The solution of the first inequality is the shaded area below the solid line
`y=4`

so

The inequality is

`y\leq 4` ----> first inequality

Second inequality

The solution of the second inequality is the shaded area above the solid line that pass through the points (0,-2) and (1,0)

Find the equation of the solid line

Find the slope

`m=(0+2)/(1-0)=2`

the y-intercept b is

`b=-2`

The linear equation in slope intercept form is equal to

`y=2x-2`

so

The second inequality is

`y\geq 2x-2` ---> second inequality

Third inequality

The solution of the third inequality is the shaded area above the dashed line that pass through the points (0,1) and (-4,4)

Find the equation of the dashed line

Find the slope

`m=(4-1)/(-4-0)=-(3)/(4)`

the y-intercept b is

`b=1`

The linear equation in slope intercept form is equal to

`y=-(3)/(4)x+1`

so

The third inequality is

`y>-(3)/(4)x+1` ----> third inequality

The system of inequalities is

`y\leq 4`

`y\geq 2x-2`

`y>-(3)/(4)x+1`