Question

Solve by 'Elimination by equating Coefficients' method

$3.) \: a {}^{2} x + b {}^{2} y = c {}^{2}$
;

$b {}^{2} x + a {}^{2} y = d {}^{2}$

Class 10


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Answer 1

Given Equation is a^2x + b^2y = c^2 ------ (1)

Gievn Equation is b^2x + a^2y = d^2 ------- (2)

On solving (1) * a^2 & (2) * b^2, we get

= > a^4x + b^2a^2y = c^2a^2

= > b^4x + b^2a^2y = d^2b^2

--------------------------------------------

(a^4 - b^4)x = (c^2a^2 - d^2b^2)

x = (c^2a^2 - d^2b^2)/a^4 - b^4.

Substitute x in (2), we get

= > b^2x + a^2y = d^2

= > a^2y = d^2 - b^2x

= > a^2y = d^2 - b^2[c^2a^2 - d^2b^2/a^4 - b^4]

= > y = d^2 - [b^2(c^2a^2 - d^2b^2/a^4 - b^4)]/a^2

= > y = d^2(a^4 - b^4) - b^2(a^2c^2 - d^2b^2)/a^2(a^4 - b^4)

= > y = a^4d^2 - b^4d^2 - b^2a^2c^2 + b^4/(a^2(a^4 - b^4))

= > y = a^4d^2 - a^2b^2c^2/a^2(a^4 - b^4)

= > y = a^2(a^2d^2 - b^2c^2)/a^2(a^4 - b^4)

= > y = (a^2d^2 - b^2c^2)/(a^4 - b^4).

Hope this helps!