Question

Which system of linear inequalities has the point (2, 1) in its solution set?

Answer 1

Answer:

$y\leq-x+3$

$y\leq \frac{1}{2}x+3$

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

Verify each system of inequalities

case 1) we have

$y$ ----> inequality A

$y\leq \frac{1}{2}x+3$ -----> inequality B

Verify if the ordered pair (2,1) is a solution of the system

Inequality A

$1$

$1$ ----> 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

$y\leq-\frac{1}{2}x+3$ ----> inequality A

$y< \frac{1}{2}x$ -----> inequality B

Verify if the ordered pair (2,1) is a solution of the system

Inequality A

$1\leq-\frac{1}{2}(2)+3$

$1\leq2$ ----> is true

so

The ordered pair satisfy the inequality A

Inequality B

$1< \frac{1}{2}(2)$

$1< 1$ -----> 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

$y\leq-x+3$ ----> inequality A      

$y\leq \frac{1}{2}x+3$ -----> inequality B

Verify if the ordered pair (2,1) is a solution of the system

Inequality A

$1\leq-(2)+3$

$1\leq 1$ ----> is true

so

The ordered pair satisfy the inequality A

Inequality B

$1\leq \frac{1}{2}(2)+3$

$1\leq 4$ ----> is true

so

The ordered pair satisfy the inequality B

therefore

The ordered pair satisfy the system of inequalities

case 4) we have

$y< \frac{1}{2}x$ ----> inequality A      

$y\leq -\frac{1}{2}x+2$ -----> inequality B

Verify if the ordered pair (2,1) is a solution of the system

Inequality A

$1< \frac{1}{2}(2)$

$1< 1$ ----> is not true

so

The ordered pair satisfy the inequality A

therefore

The ordered pair not satisfy the system of inequalities

Answer 2

Answer:

Your answer is Graph 3

Step-by-step explanation:

Look at the picture I included.

It is this graph because:

- Graph D is incorrect because you cannot have a point on a dashed line

- Even though for Graph D the point (2, 1) has a solid and dashed line running through it, you cannot plot a point on a dashed line, regardless if there is another solid line running through it.

- For options A and B, (2, 1) lands on a dashed line

- Your answer is option C

- This is right on edg2020 and quizlet!

I hope this helps!

- sincerelynini