Question

[elaine]

How do I solve this?

Solve for x:

ax - by = a^2
bx - ay= b^2

Solve for x:
ax + by = a^2 + 2ab - b^2
bx + ay = a^2 + b^2

Thanks

[Collin Li]

ax - by = a^2
=> ax = a^2 + by
=> x = a + by/a

bx - ay = b^2
=> ay = bx - b^2
=> y = bx/a - b^2/a

Sub y into x:
x = a + b/a(bx/a - b^2/a) = a + b^2*x/a^2 - b^3/a^2
=> x(1-b^2/a^2) = a - b^3/a^2
=> x = [ (a - b^3/a^2)/(1-b^2/a^2) ]
=> x = [ (a^3 - b^3) / (a^2 - b^2) ]

Simplification (not required):
=> x = [ (a-b)(a^2 + ab + b^2) / (a-b)(a+b) ]
=> x = (a^2 + ab + b^2)/(a+b)
=> x = [(a^2 + 2ab + b^2) - ab]/(a+b)
=> x = (a+b) - ab/(a+b)

There might be an easier way, but that's how you solve the first set of equations.

[elaine]

cheers mate