Answer:
Option 2nd is correct
Step-by-step explanation:
To graph the given inequality, graph the boundary of these equations.
Use dashed line if < or > used to indicate that the boundary is not the part of the solution.
Use solid line if ≤ or ≥ used to indicate that the boundary is included in the solution.
Given the system of inequalities:
[tex]y\geq \frac{1}{2}x+1[/tex]
[tex]y>-x-2[/tex]
First graph the inequality [tex]y>-x-2[/tex].
The related equation is [tex]y=-x-2[/tex].
Since this is strict inequality '>', so the border is dotted.
x-intercept:
Substitute value y=0 in [tex]y=-x-2[/tex] to solve for x
0 = -x-2
x = -2
x-intercept = (-2, 0)
y-intercept
Substitute value x=0 in [tex]y=-x-2[/tex] to solve for y
y= 0-2
y = -2
y-intercept = (0, -2)
Since the sign of inequality is >, therefore the point on the line does not contains the solution set and shade the upper half of the line.
Now, graph the inequality [tex]y\geq \frac{1}{2}x+1[/tex] .
The related equation is [tex]y=\frac{1}{2}x+1[/tex]
Since, this inequality is '≥' not the strict one, the border line is solid.
x-intercept:
Substitute value y=0 in [tex]y=\frac{1}{2}x+1[/tex] to solve for x
[tex]0=\frac{1}{2}x+1[/tex]
[tex]-1=\frac{1}{2}x[/tex]
⇒x = -2
x-intercept = (-2, 0)
y-intercept
Substitute value x=0 in [tex]y=\frac{1}{2}x+1[/tex] to solve for y
[tex]y=\frac{1}{2}(0)+1[/tex]
y =1
y-intercept = (0, 1)
Since the sign of inequality is ≥ , therefore the point on this line contain in the solution set and shade the upper half of the line.
You can see the graph of these system of inequalities.
