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### Course: Algebra (all content) > Unit 6

Lesson 1: Checking solutions of two-variable inequalities# Testing solutions to systems of inequalities

Sal checks whether the ordered pair (2,5) is a solution of the following system: y≥2x+1 and x>1. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- This video is no help with the questions asked. this bit is easy enough to solve some questions but most of the questions give us a graph with some shaded area's and we are supposed to guess which one is the result of the inequalities I can get it right most of the time but some times I get it wrong and I don't know why! lets have some video's on this topic please.(15 votes)
- If the two shaded areas in the graph overlap, then any point in that dual shaded area satisfies both equations. So, if the point (3, 5) is within the dual shaded area, then it would be a correct answer.(4 votes)

- can a solution set satisfy only one inequality?(6 votes)
- This may be a bit deeper than you mean but here is the best answer I can provide.

Each inequality has it's own solution set.

But the solution set of both inequalities must satisfy both inequalities.

So you can have a solution set for each inequality, but that solution set is not the solution set for both unless the two are mathematically equivalent to one another :

E.G:

y > 1/2x + 4

y > 1/2 (x + 8)(22 votes)

- How would you shade a graph with this solution(13 votes)
- Can we have a system with one inequality and one equation?(4 votes)
- I have never seen that, so I would like to say that that is not possible. I have tried to do research as well, but no results popped up. I believe that there would technically be solutions, but you will probably never get asked a question like that.(6 votes)

- at0:37, I am a bit confused on how that worked. How is X 2 and Y 5? How do we assign solution numbers to the variables? How do we know which ones to assign? Couldn't it be X 5 and Y 2? Checking the inequalities is really difficult for me.(3 votes)
- The question is asking to check for an x,y coordinate. I think the video assumes the watcher to understand the typical structure of a coordinate point: (x, y). So x = 2 and y = 5. Not the other way around. And after that, simply substitute the values into the inequalities.(2 votes)

- can a solution set satisfy only one inequality?(2 votes)
- A solution to a system or equations or a system of inequalities must satisfy all equations/inequalities in the system. So, if a solution works in just one inequality, then it is a solution to just that inequality. It is not a solution to the system.(2 votes)

- Can you substitute x>1 in the equation? Just want to check on it.(2 votes)
- yah. definitely didn't explain:

solid lines on a graph verse the dashed lines

also didn't explain the shaded in area's lighter shade and the darker shades meaning(2 votes) - Why is Sal worried and if he is he can just ask for help and he also try out alternate methods for the awnser.(2 votes)
- Good Question But IDK(1 vote)

- For a question which lists the solutions as answers with a pair of inequalities, should you check each one in the way that is in the video or is there a shorter way to solve them? I'm taking a big math test tomorrow and don't want to get these type of questions wrong.(1 vote)
- Well, you could graph both inequalities and see where they overlap, however, it takes longer to graph. Solving is faster, especially if you know how to do it efficiently.(2 votes)

## Video transcript

Is two comma five a solution of this system? And we have a system of inequalities right over here. We have Y is greater than or equal to 2x plus 1 and X is greater than 1. In order for two comma five to be a solution of this system, it just has to satisfy both inequalities. So, lets just try it out. So when X is equal to two and Y is equal to five, it has to satify both of these. So lets try it with the first one. So if we assume X is two and Y is five, we would get an inequality that says that five is greater than or equal to two times two plus one. X is two; Y is five. This gives us five is greater than or equal to two times two is four plus one is five. Y is greater than or equal to five. That's true! Five is equal to five. So that equal part of the greater than or equal saves us. That definitely satisfies the first inequality. Lets see the second one. X needs to be greater than one. So in two comma five, X is two. So two is greater than one. So it actually satisfies both of these inequalities. So two comma five is a solution for this system.