Question

Please I need help with this

Answer 1

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Answer 2

Question 1:

We have the region given by:

`y> 2x + 1`

First we want to find an ordered pair that is not a solution, that is, evaluate the inequality in a pair (x, y) and that it is not fulfilled.

Example:

`(x, y) = (3,1)`

We replace:

`1> 2 (3) +1\\1> 6 + 1\\1> 7`

It is not fulfilled

The pair (3,1) is not a solution of
`y> 2x + 1`

Now, we want to find an ordered pair that is a solution of the region, that is, that the inequality is met.

Example:

`(x, y) = (3,8)`

We replace:

`8> 2 (3) +1\\8> 6 + 1\\8> 7`

The inequality is met.

The pair (3,8) is solution of
`y> 2x + 1`

Answer:

The pair (3,1) is not a solution of
`y> 2x + 1`

The pair (3,8) is solution of
`y> 2x + 1`

Question 2:

For this case, we must evaluate each of the options in the acad region:

Coordinate 1: (x, y) = (5,3)

Set 1:

`y> - \frac {1} {2} x + 5\\3> - \frac {1} {2} (5) +5\\3> - \frac {5} {2} +5\\3> \frac {5} {2}`

Is fulfilled.

Set 2:

`y \leq3x-2\\3 \leq3 (5) -2\\3 \leq15-2\\3 \leq13`

Is fulfilled.

Coordinate 2: (x, y) = (4,3)

Set 1:

`y> - \frac {1} {2} x + 5\\3> - \frac {1} {2} (4) +5\\3> - \frac {4} {2} +5\\3> \frac {6} {2}\\3> 3`

It is not fulfilled

Set 2:

`y\leq 3x-2\\3\leq3 (4) -2\\3\leq 12-2\\3\leq 10`

If it is fulfilled.

Coordinate 3: (x, y) = (3,4)

Set 1:

`y> - \frac {1} {2} x + 5\\4> - \frac {1} {2} (3) +5\\4> - \frac {3} {2} +5\\3> \frac {7} {2}\\3> 3.5`

It is not true

Set 2:

`y\leq 3x-2\\4\leq 3 (3) -2\\4\leq 9-2\\4\leq 7`

Is fulfilled.

Coordinate 4: (x, y) = (4,4)

Set 1:

`y> - \frac {1} {2} x + 5\\4> - \frac {1} {2} (4) +5\\4> - \frac {4} {2} +5\\4> \frac {6} {2}\\4> 3`

It is not true

Region 2:

`y\leq 3x-2\\4\leq 3 (4) -2\\4\leq 12-2\\4\leq 10`

Is fulfilled

Answer:

There is not a pair that is not a solution of both at the same time