Answer:
Step-by-step explanation:
Given the two inequalities:
[tex]y \ge 2x + 1\\ y \le 2x - 2[/tex]
To graph them, first of all, let us write their corresponding equations:
[tex]y = 2x + 1 \\y = 2x - 2[/tex]
We now find at least 2 points each which satisfy the equations to plot the graph.
Equation [tex]y = 2x + 1[/tex]:
Putting x = 0, y = 1
Putting y = 0, x = [tex]-\frac{1}2[/tex].
Two points are (0, 1) and ([tex]-\frac{1}2[/tex], 0).
Equation [tex]y = 2x -2[/tex]:
Putting x = 0, y = -2
Putting y = 0, x = 1.
Two points are (0, -2) and (1, 0).
Now, let us plot them.
Let us take a point (1, 4) and check whether it satisfies the first inequality.
[tex]4 \ge 2 \times 1 +1\\\Rightarrow 4 \ge 3[/tex]
Which is true.
So, The shaded region will be towards point (1,4).
Let us take a point (1, 4) and check whether it satisfies the second inequality.
[tex]4 \le 2 \times 1 -2\\\Rightarrow 4 \le 0\ [\bold{False}][/tex]
So, The shaded region will be opposite to point (1,4).
Please refer to the attached graph for the answer.
No solution exists for them because there is no common shaded region.
