Could Systems of Equations work here?

Could systems of equations work at the step in this screenshot?

where we’d have (x-y) (x+y) = 1, and x+y = 8, and try to solve using systems of equations. It didn’t get me the right answer and I’m failing to see what rule is being broken that makes it never work.

and how do you solve it that way?

I have no idea. I’m thinking it’s not doable. But I thought maybe I could be wrong. But I’m still leaning towards “not doable.”

It’s not quite clear what you mean by “system of equations”, since we usually refer them to linear equations. You can do it algebraically if that’s what you meant:

x + y = 8
\rightarrow x^2 + (8 - x)^2 = 1

and solve the quadratic.

1 Like

Ahhh! Yea I was thinking about this the wrong way. That solution makes sense. Yes I was thinking some algebraic solution might be there that I wasn’t quite seeing. Thanks Leaderboard!