解二元二次方程:x^2-5xy+3y^2=0 x^2+y^2+x-11y-2=0；还有一个2x-3y-1=0 2x^2-5xy+y^2+10x+12y-100=0.急得很,

Question

解二元二次方程:x^2-5xy+3y^2=0 x^2+y^2+x-11y-2=0；还有一个2x-3y-1=0 2x^2-5xy+y^2+10x+12y-100=0.
急得很,

Answer 1

2x-3y-1=0 => x = (3y + 1) / 2 ,代入另一个式子：
2x^2-5xy+y^2+10x+12y-100
= -100 + 12 y + y^2 + 5 (1 + 3 y) - 5/2 y (1 + 3 y) + 1/2 (1 + 3 y)^2
=1/2 (-189 + 55 y - 4 y^2)
=-1/2 (-7 + y) (-27 + 4 y) = 0
所以 y = 7 ,x = (3y + 1) / 2 = 11
或者 y = 27/4 ,x = (3y + 1) / 2 = 85/8
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