Answer:
The system of inequalities is
[tex]y\leq 4[/tex]
[tex]y\geq 2x-2[/tex]
[tex]y>-\frac{3}{4}x+1[/tex]
Step-by-step explanation:
In this problem we have three inequalities
First inequality
The solution of the first inequality is the shaded area below the solid line [tex]y=4[/tex]
so
The inequality is
[tex]y\leq 4[/tex] ----> 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
[tex]m=(0+2)/(1-0)=2[/tex]
the y-intercept b is
[tex]b=-2[/tex]
The linear equation in slope intercept form is equal to
[tex]y=2x-2[/tex]
so
The second inequality is
[tex]y\geq 2x-2[/tex] ---> 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
[tex]m=(4-1)/(-4-0)=-\frac{3}{4}[/tex]
the y-intercept b is
[tex]b=1[/tex]
The linear equation in slope intercept form is equal to
[tex]y=-\frac{3}{4}x+1[/tex]
so
The third inequality is
[tex]y>-\frac{3}{4}x+1[/tex] ----> third inequality
The system of inequalities is
[tex]y\leq 4[/tex]
[tex]y\geq 2x-2[/tex]
[tex]y>-\frac{3}{4}x+1[/tex]
