Solve the following system of equations by cross - multiplication method.
a(x + y) + b(x – y) = a² – ab + b²

a(x + y) – b(x – y) = a² + ab + b²

Question

Solve the following system of equations by cross - multiplication method.a(x + y) + b(x – y) = a2 – ab + b2a(x + y) – b(x – y) = a2 + ab + b2

Philoid · Accepted Answer

The given system of equations can be re - written as

ax + ay + bx – by – a² + ab – b² = 0

⇒(a + b)x + (a – b)y – (a² – ab + b² ) = 0 …(1)

and ax + ay – bx + by – a² – ab – b² = 0

⇒ (a – b)x + (a + b)y – (a² + ab + b² ) = 0 …(2)

Now, by cross – multiplication method, we have

By cross - multiplication method, we have

On taking I and III ratio, we get

On taking II and III ratio, we get