Question

Solve for x and y:
`ax - by = a^2 + b^2, x + y = 2a`

Answer 1

The given equations are
`ax - by = a^2 + b^2 `                  ………(i)
x + y = 2a                                      ………(ii)
From (ii)
y = 2a - x
Substituting y = 2a – x in (i), we get
`ax – b(2a – x) = a^2 + b^2`
`⇒ax – 2ab + bx = a^2 + b^2`
`⇒x = (a^2+ b^2 + 2ab)/(a+b) =( (a+b)^2)/(a+b)= a + b`
Now, substitute x = a + b in (ii) to get
a + b + y = 2a
⇒y = a – b
Hence, x = a + b and y = a – b.