​ Solve each of the following systems of equations by the method of cross-multiplication: x/a + y/b = a + b x/(a^2) + y/(b^2) = 2

Question

Solve each of the following systems of equations by the method of cross-multiplication:

\(\frac{x}{a}\) + \(\frac{y}{b}\) = a + b

\(\frac{x}{a^2}\) + \(\frac{y}{b^2}\) = 2

Answer 1

Method of cross multiplication

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

Given,

 \(\frac{x}{a}\) + \(\frac{y}{b}\) = a + b

\(\frac{x}{a^2}\) + \(\frac{y}{b^2}\) = 2

⇒ x = a², y = b²