00:01
Hi there, in this problem some inequalities are given and the pairs are given.
00:07
We have to determine whether the pairs are the solution to the inequality and these are the graphs that are given and we have to shade the region that is the solution to this inequality.
00:21
So let us start with the solution to this problem.
00:24
Starting with the first inequality that is we have.
00:31
So the first inequality.
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Is x plus x minus 3y is less than equal to negative 6.
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The first pair is given 4 .5.
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So here we have x comma y is equal to 4 .5.
00:55
This means that 4 minus 3 multiplied by 5 would be less than or equal to negative 6.
01:07
This means that 4 minus 15 that is negative 11 is less than or equal to negative 6.
01:16
Since it is a true statement, so this means that 4 .5 is a solution to the inequality.
01:30
In the part b we have negative 1, negative 2.
01:36
So x comma y is equal to negative 1.
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Negative 2.
01:41
This means that negative 1 minus 3 multiplied by negative 2 is less than or equal to negative 6.
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This gives 5 is less than or equal to negative 6.
01:59
Since it is a false statement, therefore negative 1 comma negative 2 is not a solution to the inequality.
02:14
And the second iniquality we have 4x plus y is greater than.
02:21
2 and the first pair that is given is x comma y is equal to negative 2 .5 this gives 4 multiplied by negative 2 plus 5 is greater than 2 and from here we get negative 2 plus 5 that is negative 3 is greater than 2 which is a false statement therefore the ordered pair is not a solution that is negative 2 5 is not a solution to the inequality.
03:04
The second order pair that is given is 3.
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Negative 7.
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So we equate this to x comma y.
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And this gives 4 multiplied by 3 plus negative 7 is greater than 2.
03:22
This gives 12 minus 7 that is 5 is greater than 2 since it is a true statement.
03:28
So this means that the ordered pair 3 comma negative 7 is a solution to the inequality.
03:43
Now moving on to the third inequality that we have, it is 5x plus 2y is greater than or equal to 11.
03:59
The first ordered pair that is given is 1 .2.
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So we wait this to x comma y and this gives.
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5 multiplied by 1 plus 2 multiplied by 2 is greater than or equal to 11.
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This is equal to 5 plus 4 that is 9 is greater than or equal to 11.
04:20
Since it is a false statement, therefore the ordered pair 1 .2 is not a solution to the inequality 5x plus 2 y is greater than or equal to 11.
04:35
The second order pair that is given is 2 .1.
04:46
We weight this to x comma y and this gives 5 multiplied by 2 plus 2 multiplied by 1 is greater than or equal to 11.
05:00
From here we have 10 plus 2 that is 12 is greater than or equal to 11 since it is a true statement.
05:06
So we have 2 .1 is a solution to the inequality 5x plus 2y is greater than or equal to 11.
05:22
Now moving on to the fourth inequality, that is 2x minus 2y is less than or equal to 11.
05:35
The first ordered pair that is given is 3 .4.
05:40
We equate this to x comma y and this gives 2 multiplied by 3 minus 2 multiplied by 4 is less than or equal to 11.
05:52
This means that 6 minus 8 that is negative 2 is less than or equal to 11.
05:58
It is a true statement.
06:01
Therefore we write 3 .4 is a solution to the inequality 2x minus 2y is less than or equal to 11.
06:12
The second order pair that is given is 4 .0.
06:23
We wait this to x comma y and this gives 2 multiplied by 4 minus 2 multiplied by 0 is less than or equal to 11.
06:35
From here we have 8 is less than or equal to 11.
06:39
It is a true statement.
06:41
Therefore we can say that 4 .0 is a solution to the end.
06:53
Inequality 2x minus 2y is less than or equal to 11...