SOLUTION: Find the points of intersection of the line 3x+2y=10, with the curve x^2-xy+y^2=21

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Question 868572: Find the points of intersection of the line 3x+2y=10, with the curve x^2-xy+y^2=21
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
3x%2B2y=10
2y=10-3x
y=5-%283%2F2%29x
Substitute,
x%5E2-xy%2By%5E2=21
x%5E2-x%285-%283%2F2%29x%29%2B%285-%283%2F2%29x%29%5E2=21
x%5E2-5x%2B%283%2F2%29x%5E2%2B%2825-15x%2B%289%2F4%29x%5E2%29=21
%2819%2F4%29x%5E2-20x%2B25=21
%2819%2F4%29x%5E2-20x%2B4=0
19x%5E2-80x%2B16=0
%28x-4%29%2819x-4%29=0
Two solutions:
x-4=0
x=4
Then,
y=5-%283%2F2%294
y=5-6
y=-1
and
19x-4=0
19x=4
x=4%2F19
Then,
y=5-%283%2F2%29%284%2F19%29
y=5-6%2F19
y=89%2F19