Question

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

Answer 1

The given equations are
x + y = a + b                                    …….(i)
ax – by = `a^2 – b^2`                              ……..(ii)
Multiplying (i) by b and adding it with (ii), we get
bx + ax = ab + `b^2 + a^2 – b^2`
`⇒ x =( ab+ a^2)/(a+b) = a`
Substituting x = a in (i), we have
a + y = a + b
⇒y = b
Hence, x = a and y = b.