(a - b)x (a + b)y = a2 - 2ab -b2, (a +b) (x + y) = a2 + b2

Leave a Comment / pair of linear equations, real numbers / By Sapling Academy

Q) Solve the following pair of linear equations:

$\frac{x}{a} - \frac{y}{b} = 0$

$a x + b y = a^2 + b^2$

Ans:

Given the equations:

$\frac{x}{a} - \frac{y}{b} = 0$ ……….. (i)

$a x + b y = a^2 + b^2$ ………….(ii)

Step 1: Let’s multiply equation (i) by b²and add to equation (ii), we get:

$\frac{x}{a} \times b^2 - \frac{y}{b} \times b^2 + a x + b y = 0 + a ^2 + b^2$ ……….. (i)

∴ $\frac{x b^2 }{a} - b y + a x + b y = 0 + a ^2 + b^2$ ……….. (i)

∴ $\frac{x b^2 }{a} + a x = 0 + a ^2 + b^2$ ……….. (i)

∴ b² x + a² x = a ( a² + b² )

∴ x (a² + b²) = a ( a² + b² )

∴ x = a

Step 2: Lets substitute x = a in equation (ii) and we get:

a x + b y = a²+ b²

∴ a (a) + b y = a²+ b²

∴ a² + b y = a²+ b²

∴ b y = b²

∴ y = b

Therefore, x = a and y = b

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