Problem

In part a, graph the solution of each system. Use…

04:29

Problem 46 Hard Difficulty

Graph the solutions of each system.
$$
\left\{\begin{array}{l}
{y+2 x \leq 0} \\
{y \leq \frac{1}{2} x+2}
\end{array}\right.
$$

Answer

$y \leq \frac{1}{2} x+2$

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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

So here we have the system of inequalities with why, plus two bucks ISS glass and they're equal to zero and what is listen or equal to one over two X Plus two, and we're going to grab the solutions for the system. And first we must look for the line of the questions. And here we will have. Why is going to be less than or equal to two bucks naked of two X? So our line is simply going to be white sequel to Negative two X, and this equation will simply be. Why does he call to 1/2 bucks close to and with this information against art graphic and our first line is going to be by is equal to negative two X So we'll have a slope of negative too, like so likes. So this is our Why is equal to negative two. Thanks no, for our green equation, we're going to have one have X plus two. So we know we have a white intercept, too, and a slow of one house, so that's going to be fun to like. So So this is our why is equal to 1/2 X plus two now to know which side of the graph is going to be shaded off. We can choose a again, choose a point. It is going to be this case, just one one and we can plug it in. Did this and the quality and that will give us one. These girls are equal to negative to, and this satisfies the conditions. So this is the part that is going to be shaded off and here we can choose the point 00 and we're going to plug it into this inequality, and that will give us zero ISS less than or equal to zero plus two. And this will leave us. But so it was less than equal to To which satisfies the condition. So this is going to be the part that's going to appreciate it off. And now we can observe where both of the graphs overlap, and this is going to be our solution

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