Solve the system of equations algebraically x^2+2y^2=10 3x^2-y^2=9

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We have to solve the system of equations:

x^2+2y^2=10...(1)

3x^2-y^2=9 ...(2)

(1) - 2*(2)

=> x^2 + 2y^2 - 3x^2 - 2y^2 = 10 - 18

=> -2x^2 = -8

=> x^2 = 4

Substitute in (2)

3*4 - y^2 = 9

=> y^2 = 3

x^2 = 4

=> x = -2 and 2

y^2 = 3

=> y = sqrt 3 and -sqrt 3

The required solutions are (2, sqrt 3),(2 , -sqrt 3), (-2 , sqrt 3), (-2, -sqrt 3)

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