SOLUTION: (4x^2)+(9y^2)=16 2x+3y=4

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Question 371715: (4x^2)+(9y^2)=16
2x+3y=4
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
This is the intersection of a line with an ellipse.
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1.%284x%5E2%29%2B%289y%5E2%29=16
2.2x%2B3y=4
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From eq. 2,
2x=4-3y
4x%5E2=%284-3y%29%5E2
4x%5E2=16-24y%2B9y%5E2
Substitute into eq. 1,
%2816-24y%2B9y%5E2%29%2B9y%5E2=16
18y%5E2-24y=0
6y%283y-4%29=0
Two solutions:
6y=0
highlight%28y=0%29
Then from eq. 2,
2x%2B0=4
highlight%28x=2%29
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3y-4=0
3y=4
highlight_green%28y=4%2F3%29
Then,
2x%2B3%284%2F3%29=4
2x%2B4=4
2x=0
highlight_green%28x=0%29
The two intersection points are (2,0) and (0,4%2F3).
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