Question

Solve for x and y:

`(bx)/a - (ay)/b + a + b = 0, bx - ay + 2ab = 0`

Answer 1

The given equations are:

`(bx)/a - (ay)/b + a + b = 0`

By taking LCM, we get:

b²x – a²y = –a²b – b²a   ...(i)

And bx – ay + 2ab = 0

bx – ay = –2ab   ...(ii)

On multiplying (ii) by a, we get:

abx – a²y = –2a²b   ...(iii)

On subtracting (i) from (iii), we get:

abx – b²x = 2a²b + a²b + b²a = –a²b + b²a

⇒ x(ab – b²) = –ab(a – b)

⇒ x(a – b)b = –ab(a – b)

∴ `x = (-ab(a - b))/((a - b)b) = -a`

On substituting x = –a in (i), we get:

b²(–a) – a²y = –a²b – b²a

⇒ –b²a – a²y = –a²b – b²a

⇒ –a²y = –a²b

⇒ y = b

Hence, the solution is x = –a and y = b.