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# Systems of equations with elimination: King's cupcakes

Sal uses simple elimination to figure out how many cupcakes are eaten by children and adults. Created by Sal Khan.

## Want to join the conversation?

• I understand the math and the method. I graphed all of the problems with no trouble and I got the correct answers from the x and y axes. What I don't understand is how this works. It seems almost magical. Two lines intersect and Ka-Boom, you have the two solutions. I feel I am missing something important but I can't see it. That's why It seems magical.
• When you solve a system of equations, the whole purpose is to find how the 2 equations relate to each other, and whether or not they have a common solution. The common solution is the point where the 2 lines intersect because it is a point that sits on both lines.
• I love to drink my cupcakes ()
• I don't understand why Sal over complicated this. Within the first 5 seconds of seeing " 500a + 200c = 2900" and "500a + 300c = 3100", I knew the answer. I found this by observing the difference between the two equations. Let me explain, in both equations, 500a does not change, it stays the same throughout. which means that the only difference between the two equations is that the amount of C's or children.
Because of that, I was able to tell that 1c =2, because adding 100c, with A (or Adults) remaining static, added 200 to the final product. which mean that c was a variable of 2. Once I knew this, I went back to the first equation(500a + 200c = 2900), plugged in 2 for c, subtracted 400 from 2900, then divided 2500 by 500, which equals 5, the variable of A. So I ask you, is this a special occurrence that just happens to work for a few equations? Or if not, why not just use this uncomplicated way, which you can do in your head?
• Because he is teaching an algebraic method to solve a problem. Different people use different methods to solve equations. This is part of an 8th grade math curriculum enhancement. So while it seems easier to solve in your head, it is only that easy once you have learned how to do it....like he explained here :)
• Just to let you know Sal can draw like crazy. Does he only use the computer? I tried but my work is all sloppy!
• You can use specialized drawing tablets with a stylus to imitate drawing on a real paper, which is how all of these videos are made.
• Sal is definitely human, and not a robot, cause humans make mistakes. children drink two cups...
• that was epic lol i was so focused and serious in one second even my headache is gone lol
• Ok, reading through the comments it seems like there a lot of diffewrent ways to solve systems of equation. Can someone give me a quick list? I would like to try other ways to see if I can wrap my head around it easier.

P.S.
I don't mind if there are no videos for it on Khan Academy as long as I am reffered to a explanation.
• I only know of four, substitution, elimination, graphing, and using a matrix (this does not count letting a calculator do all the work for you). Sal shows all 4 I think, but matrices are not in the Algebra I section.
• damn i saved their child and they thank me by having brunch._.
• haha so true
• To me the substitution method seems much more intuitive. I actually don't understand at all why you can suddenly just subtract one of the equations from the other? Like I get why he got the answer, but it doesn't seem logical to me why subtracting one from the other would even get you that answer. Can anyone explain?
• By now, you have solved many individual equations by subtracting the same value from both sides of the equation. This is a basic property of equality. As long as we add/subtract the same / equal value to both sides of an equation, then we have an equivalent equation.

Since the 2 sides of an equation are equal value, you are just applying this property. You are subtracting an equal value from both sides of the equation. The equal values just look different.

Hope this helps.