Answer:
y > 2x - 4 and y ≤ [tex]\frac{x}{2}-1[/tex]
Step-by-step explanation:
In this question we will find the equations of the lines first then decide the inequality sign.
Dotted line in the graph passes through two points (2, 0) and (0, -4)
Let the equation of the line is y = mx + c
Where m = slope and c = y-intercept
Slope (m) of the line will be = [tex]\frac{y-y'}{x-x'}[/tex]
m = [tex]\frac{0+4}{2-0}[/tex]
m = 2
y-intercept of the line = (-4)
So, equation of the line will be y = 2x - 4
Now we see the shaded area is above the dotted line so inequality will be
y > 2x - 4
Now for the bold line
Let the equation of this line is y = m'x + c'
This line passes through points (2, 0) and (0, -1)
then slope of the line m' = [tex]\frac{y-y'}{x-x'}[/tex]
m = [tex]\frac{0+1}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]
y-intercept = c = -1
Then equation of the line will be
y = [tex]\frac{x}{2}-1[/tex]
Since shaded area is below the bold line therefore, inequality sign will be "less than equal to"
Inequality of the bold line will be y ≤ [tex]\frac{x}{2}-1[/tex]
System of the linear inequalities will be
y > 2x - 4 and y ≤ [tex]\frac{x}{2}-1[/tex]
