Problem

Graph the solutions of each system. See Example 4…

04:38

Problem 29 Medium Difficulty

Graph the solutions of each system. See Example 4.
$$
\left\{\begin{array}{l}
{x-y<4} \\
{y \leq 0} \\
{x \geq 0}
\end{array}\right.
$$

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

we have the system off inequalities X minus one. Listen for why lesson or able than zero and X greater or equal than Ciro? So we started by graphing the boundary lines. Andi The question of the first round of relying ISS X minus one. It would four instance of what this is strict. This name is stature. The second bond relying is given by the equation. Why you want to see real and it's a solid line since is less than or equal. And the third boundary line has equation exit with zero any solid again, since the inequality has a greater or equal now the this found the relying. It's just a vertical line that go through the value Way with zero. So, in fact, this one is Oh, sorry on a recent life, So that means that this is the X axis and the third boundary line. This one is a vertical line and go through the value except with the serial. So this is the Y axis. Then we only need more information to craft the first boundary line. In order to do that, we will check for the X and Y intercept. So we have the line with equation X minus y ableto floor. And the X intercept is the point with coordinate. Why equal to zero? And if we replace in the equation, we could x equal to four. So the X intercept is the point for cereal and the Y intercept is the point of sex. Coordinate disabled to Ciro. And if we replace in the equation, we will get why it took minus for. So the Y intercept is the point cereal minus four. Then now we can graph all off the bounder reliance. So this with the graph and remember that the X axis and y axis are given by art to boundary line. So we have in blue we have the X axis. So on green, we have the y axis. Now, in order to roll the boundary line for the first inequality, we're gonna use sticks. And why intercept? So we have the X intercept is the point 40 and the Y intercept is a point serial minus four. So the wonderland go through those two points so we will get this so many draw again X axis on. This is the X intercept. Great. So now we need to, uh, identified the region given by each of the inequalities. And in order to do that, we're gonna use the test point. Okay. Now, for the for the inequality, let's start with the inequality X great and earn equal than zero. That means that the region given by this inequality is to the right off the y axis. So it's this one here, this using for the inequality. Why, less than or equal to zero? Those are all the point that are under the X axis. So is this region here now to identify the region for the blood for the inequality X minus one less than four. Oh, and this line was dashed. So it's like this. Okay, we're going to use the test point and has to be a point that does not belong toe the line bounder, relying off the inequality. So, for example, we can use the point 00 since the origin does not belong to this life. If we replace about you here, we will get zero minus your less than four. And this is true. Since you are my serious zero and east listen four. So that means that for the third. Inequality, in fact, is the first positive. It doesn't matter. The region is the one that contained the origin. So is this one here? And the solution region for the system is intersection off the three regions. So is this region. Here are these two solid line. These two point does not belong. And this Dutch like here

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