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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
