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Alright, what I like to do to show you is how to solve a system by graphene.
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And if I'm looking at these two equations, there's two ways that we can, that we've shown how to graph an equation.
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One is by graphene, the slope intercept form, and the other way is finding the, both the y and the x intercepts, and then connecting them and finding the graph.
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So I'm going to use both ways to go and graph these equations.
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So I'm looking at this equation. I see that this equation is going to be very simple for me to put the y form.
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So I'm going to go and put this over here, 3x plus y equals 15.
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And if I want to graph an equation using y equals mx plus b form, all I need to do is solve for my y.
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So what I'm going to do is I'm going to subtract the 3x on both sides.
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Now I have it in y equals a negative 3x plus 15. And that is in my form of y equals mx plus 3.
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So therefore I will be able to graph this equation using my previous forms.
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This problem over here, I can still solve for y.
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And it won't be a problem for me. I'll have to do a subtract, a negative 2x, and then divide by negative 5.
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However, another way to graph these is you can also find the x and y intercepts and then just connect them.
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So let's go and do that as well.
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So if I want to find the x intercept and the y intercept, a quick reminder, the x intercept is really graph across the x axis.
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So therefore your y value is going to be 0.
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So I'm going to plug in a 0 and for y. So I get 2x minus 5 times 0 equals 10.
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2x equals 10. Divide by 2. Divide by 2. x equals 5.
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For my y intercept, it's where the graph crosses. The y intercepts in axis.
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And therefore my x value is going to be 0. So I do 2 times 0. Finds 5y equals 10.
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And therefore it becomes a negative 5y equals 10. Divide by negative 5 on both sides.
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y equals a negative 2. So therefore when I'm going to go and graph these, all I have to do is graph on the x axis 5.
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And on the y axis is negative 2 and then connect them and that's my graph.
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So I'm just going to sketch your graph. We'll try to approximate our solution.
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I understand for those of you at home if you have graph paper you'll be able to find the exact solution.
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With here I'm just going to have to go and sketch these. So the first thing is, let's do our scaling.
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And I already noticed that this is going to fly intercepted 15. So I'm going to have to go pretty high up on the y axis of 1c345678.10.
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12, 13, 14, 15, 16.
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And a quick reminder when you're solving with the y intercept form, what you want to first do is, I'm starting to slope intercept form.
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What you want to first do is find y-interred. Show it's what the y intercept is, which is our b. So I'm going to go all the way up to 15.
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And then the next thing is you're going to want to find your slope. And my slope is our m. And notice our slope here is a whole number.
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But usually when we're graphing it we want to have it as a fractional form. Well since it's a whole number to put it in fractional form, I'm going to put it over 1.
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Therefore what this is telling me if you guys remember slope can also be red as rise of a run. So I'm going to rise negative 3, which would be down.
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And then I'm going to run, go over 1. And I'm just going to continue this pattern down 3, over 1.
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So roughly my graph is going to be in that one. And then for this one, if you solve for your x and y axis, the same thing.
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So you just go to x equals 5, 1, 2, 3, 4, 5. And then y equals negative 2. And then all I do is I connect those two points.
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And I'm not going to proximate where this would be, but I would assume that our maybe our intersection point is at 6, 1.
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I just wanted to give you guys a rough sketch of what our graphs would look like. But our intersection point is going to be roughly right there.
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So obviously with some graph paper, you'll be able to make a closer determination. But I just want to make sure you guys, when you're giving a system equations, you can solve for y and graph in this method.
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Or you can also just find your x and y intercept for each graph and they connect me as this method. So that's why we solve a system equation by graphing.