 This video will talk about solving systems of equations applications. This first one is a data that we will have to use regression. It talks about percentage of renewable energy produced using geothermal and wind is given in this table. When you look at this data, we want to put this into our calculator and I'm going to teach you something new with this. Come over to stat in our calculator and then edit. And I've already put in the geothermal and the wind, but I want to remind you how to put things in. So I want to clear out my data in L1, so I arrow up to L1, clear, and then enter. We need to talk about L1. L1 is going to be our X values, but you see that this says 2003 and there's nowhere where it tells us since what year. We're going to let this be year zero. 2004 will be one year later and 2005 is two years later and very carefully looking, we know that 2007 is four years later. So that's what I want to put into L1. So zero and then enter, one, enter, two, enter, four, enter. If you wanted to do this with me, you'll want to pause right now so you can put in the L1. L2 would be geothermal and wind would be L3. We want to find a model. To find a model, remember what we do is we want to look at it first and to see what it kind of looks like. So we're going to go to Y equal and we're going to arrow up to plot one. We have to turn our plot one and plot one, watch this, second Y equal. Then if I look at plot one, press enter, then it tells me that I'm going to have X is in L1, Y is in L2, and there are going to be boxes on my graph. And if I do zoom nine, you'll notice that I'll only get one line or one set of dots. I want to see the other set of dots for the other line so I have to come back into second Y equal. Arrow down to plot two, and I want to enter. Here, I need to arrow down until I get to, my X list is in L1. But my Y list for the wind is in L3. So I need to come in here and say second, three. Because if you see above the three in blue, it says L3. So then notice it changed it to L3. And then I want it to be a different mark so I can tell the difference between my points. So I'm going to arrow down here to the mark and then arrow over to the plus and then enter. I have put plot two on, press enter. And then when I do zoom nine, it will show me both. Here's the first set and here's the second set. So let's find the equation. Stat, remember over to calculate and option four. And when we do linear regression, it's going to do automatically L1 and L2. So this is geothermal, we'll call it g of t. So if I come into Y equal and I say negative 0.072X, plus 5.426, and if I graph, now I will see my line on top of my data and see that it is pretty close. Now here's the second trick. L3 is my wind, but when I go and do the calculating this linear regression, I go over to calculate, I still choose linear regression. But before I press enter, I have to tell it that I want it to be the ordered pair I do parentheses above your eight. And then second one will be L1. And then ordered pairs have a comma in the middle. And then second three will be L3. And then close the parentheses. That tells it what ordered pair I want it to calculate. And now I can press enter and I find out that W of t for wind is equal to 0.736 t plus 1.592. Put that into my Y equal, press enter to get to Y2. 0.736X plus 1.592 and graph, I can see my two lines. Now it says graph the model on the same set of axes and then estimate two types of energies will be the same. Well, we know from graphing systems that they'll be the same when they intersect. So I'm going to draw my graph here and I'm going to assume that I've already changed my window because notice I can't see the intersection point over here. So I will have to go into my window. I need more x's, so I need x max to be bigger. I'm going to say 10 and now I can graph again and I get a graph that shows the intersection point. And remember intersection is second trace option five. And you can enter three times. Enter, enter, enter. And that tells me that I have t in my case instead of x. 4.74 or 7.5 if I round it. And the outputs are 5.08. And let's make sense of that. That means t is years. So that's going to be four years or we'll say five years after 2003 or in 2008. Renewable energy will equal 5.08% since it was percentage of renewable energy.