Question

i need help

Answer 1

go ahead and post it and I'm sure someone would be willing to help you out. :)

Answer 2

from algebra

Answer 3

sure thing, I've seen people handling questions from Kindergarten all the way up to Calculus 3 before. So I'm sure Algebra is just fine. :)

Answer 4

ax+by =a-b
bx +ay =a+b

Answer 5

you need to solve for x and y correct?

Answer 6

yes

Answer 7

Well, I would personally go with elimination for this one... multiply the first equation by b and the second equation by a, which yields
\[abx + b^2 y = ab - b^2\] \[abx + a^2 y = a^2 + ab\]

Answer 8

go ahead.

Answer 9

Then, subtracting gives you \[(abx + b^2 y) - (abx + a^2 y) = (ab - b^2) - (a^2 + ab)\]

Answer 10

Which is just \[(b^2 - a^2)y = -b^2 - a^2\] simplifying to \[y = \frac{-b^2 - a^2}{b^2 - a^2} = - \frac{b^2 + a^2}{b^2 - a^2}\]

Answer 11

Granted it looks awful, but it's just math... :)

Answer 12

To get the x we need to plug the y back into one of the two equations (either one, it doesn't matter), so \[ax + b(-\frac{b^2 + a^2}{b^2 - a^2}) = a - b\] so working it all out \[ax = a - b + \frac{b^3 - a^2b}{b^2 - a^2}\] or \[x = 1 - \frac{b}{a} + \frac{b^3 - a^2b}{ab^2 - a^3}\]