Answer:
Step-by-step explanation:
we know that
If a point is a solution of a system of linear inequalities, then the point must satisfy both inequalities of the system
<u><em>Verify each system of inequalities</em></u>
case 1) we have
----> inequality A
-----> inequality B
Verify if the ordered pair (2,1) is a solution of the system
<em>Inequality A</em>
![1](https://tex.z-dn.net/?f=1%3C-%282%29%2B3)
----> is not true
so
The ordered pair not satisfy the inequality A
therefore
The ordered pair is not a solution of the system of inequalities
case 2) we have
----> inequality A
-----> inequality B
Verify if the ordered pair (2,1) is a solution of the system
<em>Inequality A</em>
![1\leq-\frac{1}{2}(2)+3](https://tex.z-dn.net/?f=1%5Cleq-%5Cfrac%7B1%7D%7B2%7D%282%29%2B3)
----> is true
so
The ordered pair satisfy the inequality A
<em>Inequality B</em>
![1< \frac{1}{2}(2)](https://tex.z-dn.net/?f=1%3C%20%5Cfrac%7B1%7D%7B2%7D%282%29)
-----> is not true
so
The ordered pair not satisfy the inequality B
therefore
The ordered pair is not a solution of the system of inequalities
case 3) we have
----> inequality A
-----> inequality B
Verify if the ordered pair (2,1) is a solution of the system
<em>Inequality A</em>
![1\leq-(2)+3](https://tex.z-dn.net/?f=1%5Cleq-%282%29%2B3)
----> is true
so
The ordered pair satisfy the inequality A
<em>Inequality B</em>
![1\leq \frac{1}{2}(2)+3](https://tex.z-dn.net/?f=1%5Cleq%20%5Cfrac%7B1%7D%7B2%7D%282%29%2B3)
----> is true
so
The ordered pair satisfy the inequality B
therefore
The ordered pair satisfy the system of inequalities
case 4) we have
----> inequality A
-----> inequality B
Verify if the ordered pair (2,1) is a solution of the system
<em>Inequality A</em>
![1< \frac{1}{2}(2)](https://tex.z-dn.net/?f=1%3C%20%5Cfrac%7B1%7D%7B2%7D%282%29)
----> is not true
so
The ordered pair satisfy the inequality A
therefore
The ordered pair not satisfy the system of inequalities