Solve the following equations in $x$ and $y$ by cross multiplications.
$(a - b) x + (a + b) y = a^{2} - 2 a b - b^{2} (a + b) (x + y) = a^{2} + b^{2}$

Open in App

Solution

$(a - b) x + (a + b) y = a^{2} - 2 a b - b^{2} \dots (1)$
$(a + b) x + (a + b) y = a^{2} + b^{2} \dots (2)$
$(1) - (2) ⟹ (a - b - a - b) x = a^{2} - 2 a b - b^{2} - a^{2} - b^{2} ⟹ - 2 b x = - 2 a b - 2 b^{2} ⟹ x = a + b, y = \frac{- 2 a b}{a + b}$

Suggest Corrections

Similar questions

Solve the following pair of linear equations.
(a−b)x+(a+b)y=a²−2ab−b²

(a+b)(x+y)=a²+b²

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

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

Solve the following pair of linear equation:

(a - b)x + (a + b)y = a² - 2ab - b²

( a + b)(x + y)= a² +b²

x

y

\begin{matrix} (a - b) x + (a + b) y = a^{2} - 2 a b - b^{2} (a + b) (x + y) = a^{2} + b^{2} \end{matrix}

Join BYJU'S Learning Program