Some Advanced Algebra… But Not Too Hard!

Hey, all… Here’s a problem from Zaher that’s real good for thinkin’ skills:

If x= y-3 and y=z^2, what is x in terms of z?

That caret, that’s shorthand for “to the power of.” So I’m gonna state it:

x = y – 3

y=z²

What you want to get is x in terms of z. Well. This ain’t really too hard. It’s just figurin’ out how to make x equal to a bit of math with a z in it instead of a bit of math with a y in it. You know what x means in terms of y. It’s y – 3. And you know what y means in terms of z. The key is, with any type of algebra, if two things are equal, you can substitute one for the other. So, since z² is equal to y, you can put it into the first equation instead of y. So:

x = z² – 3

That’s all you need to do! That’s x in terms of z. You can’t really reduce it any, and it’s what the question asked for. It just asks you to understand that, if two things are equal, you can substitute one for the other.

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