Given the set of inequalities:
-2x - 2y > 1
y ≥ -2
Let's graph the system of linear inequalities and shade the solution set.
For the first inequality, rewrite in slope-intercept form:
y = mx + b
Add 2x to both sides:
-2x + 2x - 2y > 2x + 1
-2y > 2x + 1
Divide through by 2:
[tex]\begin{gathered} \frac{-2y}{-2}>\frac{2x}{-2}+\frac{1}{-2} \\ \\ y<-x-\frac{1}{2} \end{gathered}[/tex]
Now, let's get two points from this inequality.
When: x = 1.5:
[tex]\begin{gathered} x=1.5 \\ y<-1.5-\frac{1}{2} \\ y<-2 \\ \\ \\ \text{WHen x = 0} \\ y<-0-\frac{1}{2} \\ y<-0.5 \end{gathered}[/tex]
For the first inequality, we have the points:
(x, y) ==> (1.5, -2), (0, -0.5)
Plot the points and connect the points using a dashed line.
Shade the area below the boundary region since y is less than.
• For the second inequality:
[tex]y\ge-2[/tex]
This inequality is a horizontal line at y = -2.
We can get any two points on the line:
(x, y) ==> (4, -2), (1.5, -2)
Draw a dashed line at y = 2.
