Question

# Solve for x and y: x2−y9=6,x7+y3=5.

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Solution

## x7+y3=5, x2−y9=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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