Question

Solve the following equations by the method of cross multiplication mx-ny=m^2+n^2;x+y=2m

Answer 1

Let mx − ny = m2 + n2  → (1)         x − y =  2n Multiply above equation with n, we get nx − ny = 2n2  → (2) subtract (2) from (1) mx − ny = m2 + n2 nx − ny = 2n2  −     +      −    (m − n)x = m2− n2 ⇒ (m − n)x = (m − n)(m + n) ∴ x = (m + n) Put x = (m + n) in   x − y =  2n ⇒ (m + n) − y =  2n ⇒ (m + n) − 2n =  y ∴ y = (m − n)