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What are the points of intersection of 3x -2y equals 1 with 3x squared -2y squared plus 5 equals 0?
Wiki User
∙ 10y ago
3x - 2y = 1 => 3x = 2y + 1 => x = (2y + 1)/3
Substitute this value in the other equation:
3*[(2y + 1)/3]2 - 2y2 + 5 = 0
3*[4y2/9 + 4y/9 + 1/9] - 2y2 + 5 = 0
4y2/3 + 4y/3 + 1/3 - 2y2 + 5 = 0
Multiplying through by 3, gives
4y2 + 4y + 1 - 6y2 + 15 = 0
2y2 - 4y - 16 = 0
y2 - 2y - 8 = 0
(y - 4)*(y + 2) = 0
So y = 4 or y = -2
when y = 4, x = (2*4 + 1)/3 = 9/3 = 3
and
when y = -2, x = (2*-2 + 1)/3 = -1
So the points of intersection are (3, 4) and (-1, -2)
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∙ 10y ago
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