yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Setting up a system of equations from context example


2m read
·Nov 11, 2024

In this video, we're going to 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 5 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 equations—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. What I like to do is usually there's a sentence or two that describes each of the equations we want to 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? 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 is going to be equal—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 that what we see in blue is just another way of writing what we underlined in blue, and what we see in yellow is just another way of writing or expressing what we underlined in yellow up there.

More Articles

View All
Ray Dalio's Warning of a Prolonged Recession in 2022 (Stagflation Explained)
Over the past few months, many economists and investors like Ray Dalio have come out and predicted an upcoming period of stagflation in the United States. Sounds like a weird and scary term, but as the name suggests, it simply means two things occurring a…
Frogfish or Seaweed...Who's to Say! | National Geographic
As a passing fish, you’d be forgiven for confusing this frog fish with a mound of seaweed. But it would be the last mistake you probably ever make. As it turns out, the frog fish is a terrifying ambush predator. The spines on this fish act as a sort of ha…
How Big is the Moon? MM#1
How big is the moon? In the night sky, the moon seems rather small, but in reality, it really isn’t. Central Europe would easily fit under it. The surface area of the moon is huge. To give you some perspective, it’s as big as the whole European continent,…
Do You Know Yourself? - Mind Field (Ep 8)
[soft dramatic music] - Hi, I’m Michael Stevens, but who are you? Do you even know who you are? Are you your memories? - I don’t remember that. - I don’t remember that at all. - Are you the choices you make? The focus tester is actually a magician. - That…
Climate Change Efforts Must Be Practical and the Time is NOW
How do we develop climate-oriented investments that are both going to move the needle in a significant way and also generate a significant enough return for investors? Yes, well think about it. It’s your pension fund, and now because it’s your pension fu…
Why It Actually Might Be 'Survival of the Friendliest' | Nat Geo Explores
[Music] It’s a dog-eat-dog world: winner takes all, survival of the fittest. But is it really? If the biggest and baddest always win, how come there are so many more of them than them? Strength is helpful, but friendliness might actually be the key to evo…