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## Algebra 1

### Unit 7: Lesson 1

Checking solutions of two-variable inequalities# Testing solutions to systems of inequalities

CCSS.Math:

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?

- can a solution set satisfy only one inequality?(4 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)(15 votes)

- 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.(8 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.(2 votes)

- How would you shade a graph with this solution(8 votes)
- Can we have a system with one inequality and one equation?(3 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.(4 votes)

- how would you check it without the y(4 votes)
- Even though there's no y in the second inequality, you still fill in the number given for x and see if it works out.(1 vote)

- are there any practice problems for testing solutions for a system of inequalities?(3 votes)
- yes, go back a video and there it is.

(above the video, "Practice this concept")

I hope this is helpful, if it is please vote up.(3 votes)

- Can you substitute x>1 in the equation? Just want to check on it.(2 votes)
- what if a point is only in one shaded region and not in both shaded regions . would that be a solution or not a solution ?(2 votes)
- This video doesn't do shaded regions, but systems of inequalities need to have both inequalities work.

Sometimes there are other kinds of problems where they will ask if a point fits one equality AND another, or one inequality OR another. If you are asked about one inequality AND another then it is the same as a system, where it has to be where they intersect. If you are asked about one inequality OR anotherthen you only need the point to be in one of the shaded areas

I should probably say again, just normal systems need it in both.(1 vote)

- How can you find and represent solutions of systems of linear equations and inequalities?(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)

## 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.