Setting up a system of equations from context example

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.