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Shade the solution of each system of inequalities on the given graph.(a) $$\left\{\begin{array}{l}{x-y \geq 0} \\ {x+y \geq 2}\end{array}\right.$$(b) $$\left\{\begin{array}{l}{x-y \leq 0} \\ {x+y \leq 2}\end{array}\right.$$(c) $$\left\{\begin{array}{l}{x-y \geq 0} \\ {x+y \leq 2}\end{array}\right.$$(d) $$\left\{\begin{array}{l}{x-y \leq 0} \\ {x+y \geq 2}\end{array}\right.$$

Algebra

Chapter 10

Systems of Equations and Inequalities

Section 5

Systems of Inequalities

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

16:06

Shade the solution of each…

02:19

03:54

Match each equation, inequ…

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Solve each system of inequ…

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So we have this system of inequalities and we want to find the region that is being overlooked by both of them. So that will be the solution to this system of inequalities. So first full, I want to say that this equation right here this inequality is gonna be able as red. And this one over here is just gonna be label this blue. So we're gonna start off by choosing a point that is under their side two points on the other side, off the nickel of the first inequality. So I'm gonna choose a point to commerce zero. So that point too, Coma zero. So I'm gonna start substituting this value to see whether or not this checks with the first inequality. So this will be too minus zero is greater than or equal to zero is that we know That, too, is, in fact, greater than zero. So this point checks. This point is located over here in this side of the inequality. And so for this specific inequality, this is a solution region. Now I'm gonna start off working with the next inequality, which is just explodes. Why it's greater than or equal to zero and I'm gonna choose the point that it's either this or the side. So when it was a 0.0 come I want which make your now I'm gonna substitute it back into the inequality. So this will be this 0.0. Come on, one. So in our inequality, we have zero plus one You square then or equal due to. So we know that one is not greater or equal to two. So this value doesn't check with the inequality. Therefore, it this is not the right answer are shaded region. For this, inequality would be the other side because we already checked that one. Therefore, the other one must be the solution. And so, the region in which this sue inequalities are overlapping, which is this one shaded in black. Just just the color to make sure that you can see it is a solution region for decent quality. So every value that it's on this region with interest, this region, it's gonna be a solution to this system inequalities. Now, let's start working with this one. I say I already told you I'm gonna choose two different colors in this case. I'm going to say that this inequality is just gonna be. Label is red, And this one it's just gonna be leaving. This blue, you can see is the same equation, but with different inequality signs. So now we have the inequality explain is why is less than or equal share? I'm gonna choose the same point that I already used, which is to calm a zero, Which is this if you have forgotten in. So we're here because you you forget. So it's gonna be a point to Sorry, two comma zero. So now we have to minus zero slaves, then or equal to zero. So we know. In fact, that, too, is greater than zero. So this value Dawson checked inequality sign, therefore are shaded region. In this case will be this one over here. No, I'm going to start working with this blue one. And it's a Rachel you there point that I chose just for the sake of using the same information was zero comma one. So, Ciro, come on, one. So now we have the inequality explodes. Why is less than or equal to two? So we're here. We have zero plus one slaves and agriculture. We know that one is in fact, less than or equal to two. So these value does, in fact, check the inequality. So shaded region will be this one right here. Therefore, our solution to the system of inequalities will be this one. Oh, sorry. Not that one. Just this space right here. So, no, we have the inequality. Zero is place and this way and expose wise less than or equal to two. So the same points are gonna be chosen. So for the red one, we're gonna choose Sorry to come. A zero two comma zero. So, in this case, we have to minus zero straighter down are equal to zero in this. We know, too, is, in fact, greater than zero. So this value does check inequality, and we're gonna start shaving this region over here. Now, the blue one says that explains why it's less than or equal to two. So I'm gonna choose a values. You're welcome. A one zero call, my one. So in this case, we have zero plus one. It's less than or equal to two, but we know that too is greater than the one. So this value indeed checks in quality and we're looking at this region over here and her answer for the system of inequalities will be this region that is located down. Finally, we have sorry for the mess. So we have finally are less system off inequalities. This is a tradition. We're not just red and blue on the same points to comment zero, two, comma zero. So now we have X minus y is less than or equal to zero. So we have to minus zero. It's less than or equal to zero. So we're saying that too is less than or equal to zero, which is not true. Therefore, this is not the right decide the way it should be. A shading book this one All of this site is traded for the blue one. We have experts. Why is greater than two went to the same 20.0 comma one zero comma one So we have zero loves one Sorry, this should be a zero Niner six is greater than or equal to two. So we know one. It's not greater than equal to two. Therefore, this inequality it doesn't check Thus the region that we should be looking at must be This one is one over here. So are shattered region should be this one and that's it

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