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## Introduction to systems of equations

Current time:0:00Total duration:1:59

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

## 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.