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
US taxation trends in post war era | Macroeconomics | Khan Academy
[Instructor] In a previous video, we looked at this diagram over here, which shows the growth in per capita GDP since 1947, and it compares to that the growth in after-tax income of the bottom 90%. And what we said in that video is it looks like somethi…
Calculating angle measures to verify congruence | Congruence | High school geometry | Khan Academy
We have four triangles depicted here, and they’ve told us that the triangles are not drawn to scale. We are asked which two triangles must be congruent, so pause this video and see if you can work this out on your own before we work through this together.…
How to read 1098 and 1099 tax forms | Taxes and tax forms | Financial Literacy | Khan Academy
Let’s talk about a few very common IRS forms or statements that you are likely to encounter in your life. The first one of these you see right over here is called a 1098, and there are different types of 1098 forms. There’s a 1098, which is to report mort…
LearnStorm Growth Mindset: Dancer on his career journey
My name is Michael Novak. I’m 34 years old, and I’m a dancer with the Paul Taylor Dance Company in New York City. I have what I call “the recipe,” which is something that I’ve built over a number of years of dancing. The first is a cross-training program…
How Did the 'Unsinkable' Titanic End Up at the Bottom of the Ocean? | National Geographic
It took three years to build and less than three hours to sink. The most iconic shipwreck in history, the Titanic, held as the most beautiful and luxurious boat of her time. The Titanic set sail once and for all from Southampton, England, to New York City…
Ron Howard and Brian Grazer Talk 'Genius' | National Geographic
I’m Ron. I’m Brian, and we’re here to talk to you about National Geographic’s first scripted show on genius. We’re focusing on Albert Einstein: 10 episodes that encompass his entire life. We, as contemporary people in this contemporary civilization that …