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Setting up a system of equations from context example (pet weights)

Practice writing a system of linear equations that fits the constraints in a word problem.

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  • scuttlebug purple style avatar for user dh_a_ra_a
    the answer i got is the weight of the dog is 25kgs and the weight of the cat is 5kg. Is this right?
    (14 votes)
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    • hopper cool style avatar for user Eason The Bestest
      You're truly correct my good sir.

      If you are not sure, here is the process:

      Since d=5c and d=c+20, let's plug in (c+20) for d in the first equation. c+20=5c. After solving this equation with one variable, we get c=5. If cat is 5 pounds, the dog is 5 times that, so it's 25 pounds. Or you add 20 to 5 and get 25. So c=5 and d=25
      (10 votes)
  • blobby green style avatar for user ezimah.o
    how do you setup linear equations from difficult context
    (3 votes)
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    • piceratops ultimate style avatar for user Hecretary Bird
      The best thing to do here is practice. Once you start working with more convoluted problems and getting familiar with them, the process will become easier. If the problem talks about the same quantity in two different ways, it's real probable that you'll have to set up a system.
      Ex: Usnavi has to sell at least 15 apples today. He sells each apple for $3.
      In this very, very stripped down problem, you can see that the variable of how many apples Usnavi sells is represented in two ways. This means that you'll probably have to set up one equation about the number of apples Usnavi sells, and another equation about the profit Usnavi makes. Hope this answered the question.
      (9 votes)
  • blobby green style avatar for user mateodesantafe69
    Why didn’t you solve it? I think that the cat weights 5 kg and the dog weighs 25 kg.
    (3 votes)
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  • aqualine ultimate style avatar for user For Kobe, aka sad 2020 :(
    Who else finds that (some) of the videos and practices are way different.
    Example: Vid Y=mx+b
    Example: Practice: 24x2+25x−47
    ax−2
    =−8x−3−
    53
    ax−2
    (4 votes)
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  • duskpin tree style avatar for user Crystal
    How can this help me with the original question??
    (0 votes)
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    • hopper cool style avatar for user Xxx ._. xxX
      If there is no equation in a problem and you have to set it up yourself this helps. When dealing with problems, like word problems, it is good to know how to set up your own equation! Think of it as an old word problem in the 3rd grade where you had to take the numbers and put them in an equation yourself! Hope this helps!
      (2 votes)
  • aqualine seed style avatar for user jonathan medina
    even with video this is confusing!!
    (1 vote)
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    • hopper cool style avatar for user Xxx ._. xxX
      If it is confusing here you go:
      He is setting up the equation from the word problem when there is no equation to start with. He is taking the numbers there and putting them with the correct variables then he puts it with an equation made by himself, if you want to know how it can help you while actually solving a problem let me know.
      (2 votes)
  • blobby green style avatar for user Helena Tao
    I used a graph.Dog = 25,cat =5
    (1 vote)
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  • blobby green style avatar for user TristinK
    how to write a system of linear equations that fits the constraints in a word problem.
    (1 vote)
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Video transcript

- [Instructor] In this video, we're gonna get some more practice setting up systems of equations. Not solving them, but just setting them up. So we're told Sanjay's dog weighs five times as much as his cat. His dog is also 20 kilograms heavier than his cat. Let c be the cat's weight and let d be the dog's weight. So pause this video and see if you can set up a system of equation, two linear equations with two unknowns that we could use to solve for c and d, but we don't have to in this video. All right so let's do it together. So, what I like to do is usually there's a sentence or two that describes each of the equations we wanna set up. So this first one tells us Sanjay's dog weighs five times as much as his cat. So how much does his dog weigh? So his dog weighs d, so we know d is going to be equal to five times as much as his cat weighs. So his cat weighs c, so d is going to be equal to five times as much as his cat weighs. So that's one linear equation using d and c. And so what's another one? Well, then we are told his dog is also 20 kilograms heavier than his cat. So we could say that the dog's weight is going to be equal to the cat's weight plus what? Plus 20 kilograms. We're assuming everything's in kilograms, so I don't have to write the units. But there you have it, I have just set up two equations in two unknowns, two linear equations, based on the information given in this word problem, which we could then solve, and I encourage you to do so if you're curious. But sometimes, the difficult part is just to find, is to re-express the information that you're given in a mathematical form. But as you see, as you get practice, it becomes somewhat intuitive. What we see in blue is just another way of writing what we underline in blue and what we see in yellow is just another way of writing or expressing wat we underlined in yellow up there.