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Question

Solve for x and y:

x2y9=6,x7+y3=5.

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Solution

x7+y3=5, x2y9=6


On taking LCM of denominators and simplifying, we get the linear equations as
3x + 7y = 105 → (1)


9x − 2y = 108 → (2)


Multiply equation(1) with 3 , we get


9x + 21y = 315 → (3)


Now subtract (2) from (3)


9x + 21y = 315
9x − 2y = 108
----------------------
23y = 207


∴ y =20723 = 9


Put y = 9 in 3x + 7y = 105


3x + 7(9) = 105


⇒ 3x = 105 − 63 = 42


x=423=14


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