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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.

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• 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.
• 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.
• can a solution set satisfy only one inequality?
• 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)
• How would you shade a graph with this solution
• Can we have a system with one inequality and one equation?
• 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.
• at , 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.
• 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.
• can a solution set satisfy only one inequality?
• 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.
• Can you substitute x>1 in the equation? Just want to check on it.
• yah. definitely didn't explain:

solid lines on a graph verse the dashed lines