# Algebra-ish question

Voivode

## Homework Statement

I'm in a calculus course, but this isn't really a calculus question. I was wondering if:

Ax + By = Cx + Dy

Could I say A = C and B = D?

None.

None.

Mentor

## Homework Statement

I'm in a calculus course, but this isn't really a calculus question. I was wondering if:

Ax + By = Cx + Dy

Could I say A = C and B = D?
It depends on what "=" means. In the first equation, if "=" means $\equiv$ (identically equal to), then yes, A = C and B = D. Here, "identically equal to" means for any choice of x and y.

On the other hand, if "=" means just plain old "equals", then no.

Here's an example. Suppose x = 3 and y = 2. Your equation is equivalent to (A - C)x = (D - B)y, so if A = 5 and C = 3, and B = 1 and D = 4, then we have (5 - 3)3 = (4 - 1)2, or 6 = 6, a true statement, but A and C aren't equal, nor are B and D.

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Voivode
That makes sense. Thanks.