Why do we use letters like x and y to represent numbers in algebra?
In: Mathematics
If your looking for the historic reason why we picked them, I can’t help there. Probably because it is an easy way to write it out.
But, for the math reason, it’s because they represent either unknowns or variables.
A unknown is a number we don’t know yet. Think of it like a question mark. We use these in early algebra to get used to the idea. Sometimes there’s more than one, so we use x, y, z, and more letters.
But algebra isn’t that useful if it’s just looking for an unknown. That’s where variables come in.
Variables are numbers that can change. That means we can choose a number, any number, and do the math.
Take X + 1 = Y.
X can be any number, and Y will always be one more than that. We don’t know what we will choose every time we do the math, so we use variables to describe how the math will behave, instead of solving one specific problem.
Normally, we say that X means something, like time or distance, and Y is something else similar.
A classic example is figuring out how tall a tree is by measuring its shadow and your own shadow.
Its really hard to take a tape measure to a tree, but not so bad to do that with the shadow, so you measure the shadow, and your own shadow, and then you can figure out how tall the tree is.
Let’s say that your shadow is half as tall as you are. That gives us an equations.
You are twice your shadow.
You are Y.
The word Are means equals.
Twice, so 2.
Your shadow is X.
That means we can turn the sentence ‘You are twice your shadow’ into the equation Y = 2X.
Well, say the tree shadow is 10 feet tall, now we can do the math and know the tree is 20 feet tall.
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