1
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Is two comma five a solution of this system?

2
00:00:04,267 --> 00:00:06,533
And we have a system of inequalities right over here.

3
00:00:06,533 --> 00:00:12,600
We have Y is greater than or equal to 2x plus 1 and X is greater than 1.

4
00:00:12,600 --> 00:00:19,148
In order for two comma five to be a solution of this system, it just has to satisfy both inequalities.

5
00:00:19,164 --> 00:00:20,738
So, lets just try it out.

6
00:00:20,933 --> 00:00:25,267
So when X is equal to two and Y is equal to five, it has to satify both of these.

7
00:00:25,267 --> 00:00:27,067
So lets try it with the first one.

8
00:00:27,067 --> 00:00:29,467
So if we assume X is two and Y is five,

9
00:00:29,467 --> 00:00:37,400
we would get an inequality that says that five is greater than or equal to two times two plus one.

10
00:00:37,400 --> 00:00:39,467
X is two; Y is five.

11
00:00:39,467 --> 00:00:44,933
This gives us five is greater than or equal to two times two is four plus one is five.

12
00:00:44,933 --> 00:00:50,133
Y is greater than or equal to five. That's true! Five is equal to five.

13
00:00:50,133 --> 00:00:52,800
So that equal part of the greater than or equal saves us.

14
00:00:52,800 --> 00:00:57,400
That definitely satisfies the first inequality. Lets see the second one.

15
00:00:57,400 --> 00:00:59,600
X needs to be greater than one.

16
00:00:59,600 --> 00:01:03,067
So in two comma five, X is two.

17
00:01:03,067 --> 00:01:06,200
So two is greater than one.

18
00:01:06,200 --> 00:01:09,533
So it actually satisfies both of these inequalities.

19
00:01:09,533 --> 00:01:14,333
So two comma five is a solution for this system.