Answer:
[tex]y\geq x-2[/tex]
[tex]x+2y<4[/tex]
Step-by-step explanation:
step 1
Find the equation of the first inequality
Find the equation of the first solid line
we have the ordered pairs
(0,-2) and (2,0)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{0+2}{2-0}[/tex]
[tex]m=\frac{2}{2}[/tex]
[tex]m=1[/tex]
The equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=1[/tex]
[tex]b=-2[/tex] ---> the y-intercept is given
substitute
[tex]y=x-2[/tex]
Remember that
Everything to the left of the solid line is shaded
so
The inequality is
[tex]y\geq x-2[/tex]
step 2
Find the equation of the second inequality
Find the equation of the second dashed line
we have the ordered pairs
(0,2) and (4,0)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{0-2}{4-0}[/tex]
[tex]m=\frac{-2}{4}[/tex]
[tex]m=-\frac{1}{2}[/tex]
The equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=-\frac{1}{2}[/tex]
[tex]b=2[/tex] ---> the y-intercept is given
substitute
[tex]y=-\frac{1}{2}x+2[/tex]
Remember that
Everything below and to the left of the line is shaded
so
The inequality is
[tex]y<-\frac{1}{2}x+2[/tex]
Rewrite
Multiply by 2 both sides
[tex]2y<-x+4[/tex]
[tex]x+2y<4[/tex]
therefore
The system of inequalities is
[tex]y\geq x-2[/tex]
[tex]x+2y<4[/tex]
see the attached figure to better understand the problem
