Problem

Graph the solutions of each system. See Example 3…

04:17

Problem 23 Easy Difficulty

Graph the solutions of each system. See Example 3.
$$
\left\{\begin{array}{l}
{x \geq 2} \\
{y \leq 3}
\end{array}\right.
$$

Answer

$x \geq 2$

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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

Okay, so we have the system off inequalities Ex grid or enable them to. And why? Less than or equal than three. So we start with the equation of the boundary lines for the first inequality, the equation of the bond or Linus X, able to to and since the inequality, it's not a strict meaning that is greater or equal. This is a solid line for the second inequality. The wonder relying has a question. Why equal to three and again, since the inequality is less than or equal is a solid life. Now, if we take a look to the two boundary lines, we have that X equal to two. This is a vertical line, and why it was three is your personal life. So in this case, we can just draw without taking a look toe for their information. So works. We will start with the X and Y axis. I would just sit down and we're going to put this we're going toe graph. Okay, so the first line ex able to toe it's a solid line, is a vertical line and goes through X equal to two. So is this land that we have here I control it really large on the second line isn't a result a line and go through the point while you could three. So it should be this. Thank you. Okay. Now we need to use a test point in order to, uh, see which is the region. So first, it has to be a point that does not belong to any off the line. So, for example, we can use the origin, since the origin does not belong to any off the two lines. Okay, so for the first inequality, we have x credit unequal than to, so we can replace the value. This is a really off except why. And we will get cereal greater unequalled in two. If we replace the value off our point over test point. And we know that this is false. So that means that the origin does not belong to the region given by the first inequality. So the region for the first inequality should be this one here. Now for the second inequality. Why listen or equal three? If we replace our test, our test point, we will get zero lesson equaled entry. And this is true. So that means that the origin belongs to the test out to the region, given by the second inequality. So for the second inequality, we have this region here. And that means that the solution region for the system it's intersection of these two regions meaning this laying here, this lane here. We're using the line since both are solid in this region down here.

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