Problem

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

04:57

Problem 30 Medium Difficulty

Graph the solutions of each system. See Example 4.
$$
\left\{\begin{array}{l}
{2 x+y \leq 2} \\
{y>x} \\
{x \geq 0}
\end{array}\right.
$$

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

So here we have a system of inequalities, starting with two x plus. Why ISS a lesson are equal to two. Why is greater than X and X IHS greater than are equal to zero. And the first thing we'll do is look for the equation of lines and starting with our first inequality. This will give us why is less than or equal Teoh Negative two X plus two. I just subjected this two X to the other side. And here we will simply get why is equal to negative two bucks. Plus do so Our line will have a one white intercept at two and a slope off. Negative, too. And here we can easily see that will simply have. Why is equal to X, And our line here will simply give us X is equal to zero, and now we can start graphic. So our first line is going to be our why is equal to negative two X plus two. So we have a white intercept to and are negative to slope. So that's two. So from here, extending this line over So here is our why is equal to negative two x last two next is going to be our Why Physical two x And that s simply is this line right here. Why is equal to X and our last line is going to be accessible to zero and that is going to be this line. Now we can start feeding according to our and equalities and we will know which part to shade by picking a point. So for our first inequality, we can simply choose 00 and plug it into this inequality. And that will give us zero is less than or equal to zero plus two which will give us Syria is less than or equal to two which satisfies the conditions. So we can shade off this part and our necks point that we can dio IHS this point which iss 01 and we will plug it in. And this inequality which will give us one iss greater than zero which satisfies our inequality. So that's the part that we are going to shade. And lastly, our X is greater that are equal to zero will give us this shaded region. Oh, and it's important to note that our why is equal to X line is going to be a dotted line since it is a restricted inequality. So now we can to include which parts is going to be our final shaded part, and it's going to be the area where everything is overlapped and we can simply see that it is going to be this small shaded region right here.

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