Answer:


Step-by-step explanation:
step 1
<em>Find the equation of the first inequality</em>
Find the equation of the first solid line
we have the ordered pairs
(0,-2) and (2,0)
<u><em>Find the slope</em></u>
The formula to calculate the slope between two points is equal to

substitute the values



The equation in slope intercept form is equal to

we have

---> the y-intercept is given
substitute

Remember that
Everything to the left of the solid line is shaded
so
The inequality is

step 2
<em>Find the equation of the second inequality</em>
Find the equation of the second dashed line
we have the ordered pairs
(0,2) and (4,0)
<u><em>Find the slope</em></u>
The formula to calculate the slope between two points is equal to

substitute the values



The equation in slope intercept form is equal to

we have

---> the y-intercept is given
substitute

Remember that
Everything below and to the left of the line is shaded
so
The inequality is

Rewrite
Multiply by 2 both sides


therefore
The system of inequalities is


see the attached figure to better understand the problem