SOLUTION: help me to solve this two equations algebraically please 4x^2+3y^2=4 and 2x-3y^2=-3

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Question 1028985: help me to solve this two equations algebraically please 4x^2+3y^2=4 and 2x-3y^2=-3
Answer by ikleyn(52775) About Me  (Show Source):
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help me to solve this two equations algebraically please 4x^2+3y^2=4 and 2x-3y^2=-3
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4x%5E2 + 3y%5E2 = 4,       (1)
2x   - 3y%5E2 = -3.    (2)

Add the equations (1) and (2) (both sides). You will get

4x%5E2+%2B+2x = 1,   or

4x%5E2+%2B+2x+-+1 = 0.

Apply the quadratic formula. You will get two roots for x

x%5B1%2C2%5D = %28-2+%2B-+sqrt%282%5E2+%2B+4%2A4%29%29%2F8 = %28-2+%2B-+sqrt%2820%29%29%2F8 = %28-1+%2B-+sqrt%285%29%29%2F4.

Having this, substitute the found values for x into (2) and then find the corresponding values of y.