Question

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.

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

$y<-x+3$ ----> 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

$1<-(2)+3$

$1<1$ ----> 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