Problem

Graph the solutions of each system. $$ \left\{\be…

03:19

Problem 44 Hard Difficulty

Graph the solutions of each system.
$$
\left\{\begin{array}{l}
{y>-2.5} \\
{2 x-y \geq 2} \\
{x \leq 2}
\end{array}\right.
$$

Answer

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Algebra

Elementary and Intermediate Algebra

Chapter 4

Systems of Linear Equations and Inequalities

Section 5

Solving Systems of Linear Inequalities

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Video Transcript

So here we have the system of inequalities starting with why ISS greater than negative 2.5 two x minus. Why is greater than or equal to two and x issa lesson or equal to two and were asked a graph the solutions of beach system. So first we will find what equation of the line each inequalities are. So here we can simply see that we will have why is equal to negative 2.5 And here well have to x minus. Why s are equal to two? We want to isolate the y so we'll have why is greater than equal to negative two x plus two and divide one both sides and we will have Why iss a lesson or equal to two x minus one So our line will be why is equal to two X minus one And here we will simply have X is equal due to And with this information we can start graphing But so our first line is going to be Why IHS less than one about 2.5. So that's going to be here This or why is equal to negative 2.5 and next is our why is equal to two X minus one so that we we know that we have a white intercept. But I got one on a slope of to here and we can extend this like so So this is our Why is equal to to explain it one and our X is equal to two is going to be this line. Now we can start shading in our ground and we know that why is greater than oh, since it's restricted, we have our line as started like so now we can start shading paragraphs so it says greater than so. That's going to be everything that's above the line. Next ISS less than so our why is listener equal to two X minus one So we can check which part of the graph is going to be shaded by point Choosing a point in this case, we can choose 00 and we can plug it in so we will have zero. It's lesson or equal to zero minus one, and this whole have ah zero IHS less are equal to negative one, which is balls. So the graph the shaded part is going to be of this side of the graph where 00 is not in next ISS going to be greater exists lesson or equal to to, and that is going to be on the left side of to. And now we can see the part that is being overlap with the shaded areas and that is going to be at this a little triangle right here, and this is our solution.

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