Given the linear inequality 4 x + 2 3 y ≥ 6 4x+\frac23y\ge6 , determine if the following ordered pair is a solution to the inequality. ( 0 , 9 ) (0,9) ( 0 , 9 )

So in this problem, we need to determine if our ordered pair zero nine is a solution to the given inequality four x plus two thirds y is greater than or equal to six. Now I know that the zero is my x, and then the nine is my y, so let's go ahead and try this in our inequality. So we're going to have four times zero plus two thirds times nine, and nine is my y, that's gonna be greater than or equal to six. Now, four times zero, or anything times zero, is just going to give you zero. Now nine, I know is the same thing as three times three. Now I can cancel one of the three's, giving me two times three is greater than or equal to six. So we have zero plus two times three, which all just comes out to six on the left side, is greater than or equal to six on the right side. Is this a true statement? Well, yes, this actually is a true statement. Because six has to be greater than or equal to six. It's not greater than six, but it is in fact equal to six. Now something I want to mention here is, yes, this would be true. This is a solution to the inequality, but I also want to mention what the graph would look like real quick. So if we were to deal with a graph for this inequality, right, let's say that we had our line that we had, and then we had our shaded region as well. When it comes to a situation where you have the solution for your inequality, it has to be in the region. This ordered pair would actually end up somewhere on the line. So zero nine, this would actually end up somewhere on this line exactly. So this is actually one of those cases where you're not gonna end up in the region, you're going to end up on the line. And that can be a little bit of of a a suspicious territory when it comes to inequalities, but it's actually fine when it's greater than or equal to. If it was just greater than, like six is greater than six, then actually, we would not want it to end up on the line. And in this case, we would see that this is not a true statement. So that's just something to keep in mind when dealing with graphs and when dealing with inequalities in general. But in this case, you can see it is a solution. And if we were dealing with the graph, it would end up on the line. So the answer to this problem is yes. The ordered pair zero nine is a solution to this inequality.

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Linear Inequalities in Two Variables

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Multiple Choice

Given the linear inequality $4 x plus two thirds y is greater than or equal to 6$ , determine if the following ordered pair is a solution to the inequality.
$(0,9)$

Yes

Cannot be determined

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Given the linear inequality $4 x plus two thirds y is greater than or equal to 6$ , determine if the following ordered pair is a solution to the inequality.
$(0,9)$