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Answer:
(-17/3, -√38/3), (-17/3, √38/3), (4, -1), (4, 1)
Explanation:
We can subtract the second equation from 4 times the first to obtain a quadratic in x, with y eliminated.
4(x² +y² +2x) -(x² +4y² +3x) = 4(25) -(32)
3x² +5x -68 = 0 . . . . . simplify to standard form
(3x +17)(x -4) = 0 . . . . . factor
x = -17/3, +4 . . . . . . . . . solutions that make the factors zero
The corresponding values of y can be found from ...
y = ±√(25 -x(2 +x)) . . . . solve the first equation for y
For x = -17/3, we get ...
y = ±√(25 -(-17/3)(2 -17/3)) = ±√(38/9) = ±(√38)/3 ≈ ±2.05480
For x = 4, we get ...
y = ±√(25 -4(2 +4)) = ±1
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The solutions are ...
(-17/3, -√38/3), (-17/3, √38/3), (4, -1), (4, 1)