 In this video we will talk about solving systems of equations applications. So an office supply company GrabMapper sells 7 notebooks and 4 pens for 640, 2 notebooks and 19 pens for 540. So you can see the two things that we are talking about are notebooks and pens. So N I am going to say is the price of a notebook. I know how many in each case, but I don't know how much it costs. And it says find the price. And I am going to let P equal the amount of money that it takes to pay for a pen. And now let's set up the system. So the equation is going to be the cost of a notebook plus the cost of a pen is equal to the total cost. That will be for both equations. We are just using the two different situations. We have got 7 notebooks and 4 pens, so 7 times the price of a notebook plus 4 times the price of a pen will equal the total cost of 6 dollars and 40 cents. And if I want to do the second equation, that is the second situation. I have got 2 notebooks, 2 times the amount we pay for a notebook plus 19 times the price we pay for a pen will give us 5 dollars and 40 cents. Remember we can graph or we can use elimination or substitution. Substitution would be the last choice I would make here because I don't have any coefficients that are equal to 1. They are all bigger than 1. So elimination might be nice and graphing might be nice. If I want to get rid of N or P, you can see the N coefficients are smaller. It would be a little bit easier to get rid of that. So I am going to take this top equation and multiply it. I need 7 and 2, I need it to be 14 and they need to be opposite signs that I am multiplying by so I am going to multiply by negative 2 so I don't forget my negative. And the bottom equation, I am going to multiply that by positive 7. So my top equation would give me negative 14N minus 8P is equal to negative 1280 and my bottom equation would be 14N plus 133P is equal to and this would be 37.8 and when I add them my N's cancel each other out because it is negative and positive 14, positive 125P and on this side I get 25 and when I divide by 125 I find out that P is 0.2 or 20 cents for a pen. Now remember I know how much a pen is, I need to find out how much a notebook is, back up into either one of the top equations. The top one has all nice numbers, that 19 is kind of big, kind of scary. So I am going to take 7 times my N plus 4 times my P which I know to be 0.2 is equal to 6.40 and when I do that I have 7N plus 0.8 is equal to 6.4. 0, subtracting the 0.8 I get 7N equal to 5.6 and when I divide by 7 N is equal to 0.8, 0 or this is equal to 80 cents. So a notebook costs 80 cents and a pen costs 20 cents.