Problem

Graph the solutions of each system. See Example 1…

07:52

Problem 15 Medium Difficulty

Graph the solutions of each system. See Example 1.
$$
\left\{\begin{array}{l}
{x+2 y \leq 3} \\
{2 x-y \geq 1}
\end{array}\right.
$$

Answer

2 y \leq 3 \mathrm{s}

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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 X plus two away list then, or evil than three. Two X minus one. Good or equal to what? And we have for the system would have boundary lines. The first equation is X was too. Why people three and the second inequality. Give us the equation to X minus one to it and different color to its minus one. Ableto. Okay, now we're going toe graph the boundary lines. And in order to do this, uh, we're going to find the X and Y intercept, so they start with X Plus two. Why? Get what? 23 So let's say the ex intercept. So that means that we need to go see that. Why? It was to see Roe. And if we replace it here, we will get X. It was three. So the X intercept is three c. Well, now the Y intercept. We need to conceive their ex being able to see, though. And when we replaced in this equation, we will get to why equal to three. So that means that why it's equal to three over. So the Y intercept is going to be zero 3/2. Now we can do the same with the order with second bundle relying. So we have two X minus one. It was the one, Andi, we look for the X intercept. That is when? Why is it weird to Ciro? And if we take this equation and evaluate why you went to see a bit tow X equal to one that implies that X X equal to 1/2. So the ex intercept is ableto 1/2 0 and the Y intercept. We need to go see their ex being equal to Ciro. And when we replaced in the equation, we get minus one equals one. So why sit? What? To minus one? That means that the why intercept. He's a 0.0 minus. What? So let's try to make a graph here. Whatever X, Let's make this smaller. Okay, so we have X on the Y axis. Okay, so first we're gonna draw the intercept. So for the red line, we have the point three c row. So let's say that is one too this point here, So I'm gonna make the land it with vigor. So the 0.3 c well, on winning to you so wrapped in this case. Since where? Drawing first line and the Y. Intercept this cereal 3/2. So let's say that it's going to be a point around here, so we're going to make this a little bit bigger. Uh, so So there was this? No. So, Cyril through over two and 3/2 is have a 1.5. Okay, so the first line should go through these two points. Something like that. And the second line, the X intercept is 1/2 cereal, 1/2 a syrup, 1 to 5, and the Y intercept ISS Cyril minus one. So we get a line like this. Okay? Now, in order to see which region willing to concede there, we're gonna look for some test point. I'm gonna write here. So first, let's look at the region for the red line. That means for the first inequality. So we have X still way. This any more than three? This worst wantto redline. So we can consider the origin uh, Ciro zero. And when we replace here, what we get is zero listen equals three, and this is true. So that means that zero belong to the solution of this inequality. So This is the region for the red line. Now, for the blue line, we have the inequality two x minus y greater or equal to one. And in this case, if we consider the test 0.0 the origin and we replace it here what? We get a zero greater or equal, then one. And this is false. So that means that the origin does not belong to the solution original for this inequality that correspond to the present here. And that means that the solution region has to be this one here.

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