Answer:
The system of inequalities is
[tex]y\leq x+3[/tex] and [tex]y\leq -2x+3[/tex]
The solution is the shaded green area
Step-by-step explanation:
step 1
Find the equation of the inequality A
The line is solid and goes through the points negative 3, 0, negative 4, negative 1 and is shaded in below the line
Find the slope
(-3,0),(-4,-1)
m=(-1-0)/(-4+3)=1
The equation of the line is y=mx+b
we have
m=1
b=3 ----> the y-intercept (see the graph)
substitute
y=x+3 -----> equation of the solid line A
The equation of the inequality is
[tex]y\leq x+3[/tex] -----> inequality A
step 2
Find the equation of the inequality B
The line is solid and goes through the points 1, 1, 2, negative 1 and is shaded in below the line
Find the slope
(1,1),(2,-1)
m=(-1-1)/(2-1)=-2
The equation of the line is y=mx+b
we have
m=-2
b=3 ----> the y-intercept (see the graph)
substitute
y=-2x+3 -----> equation of the solid line B
The equation of the inequality is
[tex]y\leq -2x+3[/tex] -----> inequality B
therefore
The system of inequalities is
[tex]y\leq x+3[/tex] -----> inequality A
[tex]y\leq -2x+3[/tex] -----> inequality B
The solution is the shaded green area
