Which system of linear inequalities has the point (2, 1) in its solution set?
y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 on a coordinate plane, 2 lines are shown. the first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). everything below the line is shaded. the second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). everything to the left of the line is shaded.
y less-than negative one-half x + 3. y less-than one-half x. on a coordinate plane, 2 lines are shown. the first solid straight line has a negative slope and goes through (0, 3) and (4, 1). everything below the line is shaded. the second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). everything below and to the right of the line is shaded.
y less-than-or-equal-to negative x + 3. y less-than-or-equal-to one-half x + 2 on a coordinate plane 2 solid straight lines are shown. the first line has a positive slope and goes through (negative 4, 1) and (0, 3). everything below the line is shaded. the second line has a negative slope and goes through (0, 3) and (3, 0). everything below and to the left of the line is shaded.
y less-than one-half x. y less-than-or-equal-to negative one-half x + 2 on a coordinate plane, 2 straight lines are shown. the first solid line has a negative slope and goes through (0, 2) and (4, 0). everything below the line is shaded. the second dashed line has a positive slope and goes through (negative 4, negative 2) and (0, 0). everything below the line is shaded.

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

----> inequality A

-----> inequality B

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

Inequality A

----> 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

Inequality A

----> is true

so

The ordered pair satisfy the inequality A

Inequality B

-----> 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

Inequality A

----> is true

so

The ordered pair satisfy the inequality A

Inequality B

----> 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

Inequality A

----> is not true

so

The ordered pair satisfy the inequality A

therefore

The ordered pair not satisfy the system of inequalities

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