以知x^2+xy=3,xy+y^2=-2求:(3)2x^2-xy-3y^2的值

因为，
x^2+xy=3----(1)
xy+y^2=-2---(2)
2*(1)-3*(2)得：
2*（x^2+xy)-3*(xy+y^2)=2*3-3*(-2)=12----(3)
式（3）的左边打开有，
2x^2-xy-3y^2=12
所以，
所求的值为12

x^2+xy=3 .....(I)
xy+y^2=-2 .....(II)

2x^2-xy-3y^2 = 2*(I) - 3*(II) = 2*3 - 3*(-2) = 12

x^2+xy=3 (1)
xy+y^2=-2 (2)
(1)*2得2x^2+2xy=6
(2)*3得3xy+3y^2=-6
相减
2x^2+2xy-3xy-3y^2=6-(-9)
2x^2-xy-3y^2=12

x^2+xy=3 ①
xy+y^2=-2 ②
①*2-②*3得
2(x^2+xy)-3(xy+y^2)=2x^2-xy-3y^2=2*3-3*(-2)=12

2x^2+2xy=6
-3xy-3y^2=6
相加
2x^2-xy-3y^2＝12