Solve the following pair of linear equations: x/a – y/b =0, a x + b y = a2 + b2

Question

Q) Solve the following pair of linear equations:

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

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

Sapling Academy · Accepted Answer

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 b2  and add to equation (ii), we get:

$\frac{x}{a} 	imes b^2 - \frac{y}{b} 	imes b^2 + a x + b y = 0 + a ^2 + b^2$ ........... (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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