About this video
The video checks whether the point (2, 5) is a solution of the system y >= 2x + 1 and x > 1. It substitutes x = 2 and y = 5 into each inequality and shows that both are true, so the point is a solution of the system.
You'll be able to
- test whether an ordered pair is a solution of a system of inequalities by substituting it into each inequality.
- explain why a point must satisfy every inequality in a system to be a solution.
- use the 'or equal to' part of >= to decide whether a boundary point counts.
Key words
- system of inequalities
- Two or more inequalities that must all be true at the same time.
- solution of a system
- A point (x, y) that makes every inequality in the system true.
- greater than or equal to
- The symbol >= means the left side can be bigger than or exactly equal to the right side.
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.
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