 What you need to know

Things to remember:

• When combing variables, we are adding, subtracting, dividing, and multiplying as usual, we just have to put our numbers in first.

Before we start, what is a variable? A variable is something that varies, it changes. So, “variable” is just a fancy word for something that changes. Here, we are going to look at combining two things that change, and how they affect each other.

$$x+ y = 5$$

Here, our variables are $x$ and $y$, they can change. How do I know they can change, you ask? Well, let’s think about what it is saying. This is equation is telling us that “something plus something equals 5”. Well, that’s easy, $1+4=5$.

$x=1$         $y=4$

$$1 + 4 = 5$$

But wait, $2+3=5$ as well.

$x=2$         $y=3$

$$2 + 3 = 5$$

$x$ and $y$ are variables, they can change. There isn’t just one answer: Notice also how as $x$ gets bigger, $y$ gets smaller. Does this always happen? What about if we’re subtracting?

$$x - y = 3$$

What is this telling us this time? “Something minus something equals 3.” Well, $7-4=3$.

$x=7$         $y=4$

$$7 - 4 = 3$$

But wait, $11-8=3$ as well.

$x=11$       $y=8$

$$11 - 8 = 3$$

So, our $x$ and $y$ are changing, but how does one affect the other? Notice how as $x$ gets bigger, so does the $y$. Why do you think that is? Think about what subtraction means.

$$x\times y = 36$$

What is this telling us this time? “Something multiply something equals 36.” Well, $3\times12=36$.

$x=3$         $y=12$

$$3\times12 = 36$$

But wait, $2\times18=36$ as well.

$x=2$         $y=18$

$$2\times18 = 36$$

So, our $x$ and $y$ are changing, but how does one affect the other? Notice how as one gets bigger, the other gets smaller. Why do you think that is?

Let’s look at division now.

$$x\div y = 4$$

What is this telling us this time? “Something divided by something equals 4.” Well, $20\div5 =4$.

$x=20$       $y=5$

$$20\div5 =4$$

But wait, $24\div6 =4$ as well.

$x=24$       $y=6$

$$24\div6 = 4$$

So, our $x$ and $y$ are changing, but how does one affect the other? Notice how as $x$ gets bigger, $y$ gets smaller.

Example Questions

$x$              0          1          2          3          4          5          6

$y$              6          5          4          3          2          1          0

As one gets bigger, the other gets smaller

$x$              6          12        18        24        36        42        48

$y$              1          2          3          4          5          6          7

As $x$ gets bigger, so does y[/latex