中四聯立方程問題

1:
x-y-1=0.....(1)
x^2-xy+y^2=7.....(2)


From (1):


x = y+1 ,sub it to (2):


(y+1)^2 - (y+1)y + y^2 = 7


y^2+2y+1 - y^2 - y +y^2 = 7


y^2 + y - 6 = 0


(y+3)(y-2) = 0


y= - 3 , sub it to (1) , x = - 2


y = 2 , sub it to (1) , x = 3


2:
x-4y-6=0 .....(1)
x^2+2xy-36=0 .....(2)


From (1), x = 4y+6 , sub it to (2)


(4y+6)^2 + 2(4y+6)y - 36 = 0


(2y+3)^2 + (2y+3)y - 9 = 0


4y^2 + 12y + 9 + 2y^2 + 3y - 9 = 0


6y^2 + 15y = 0


2y^2 + 5y = 0


y(2y + 5) = 0


y = 0 , sub it to (1) : x = 6


y = - 5/2 , sub it to (1) : x = - 4


3:
y=2x^2-3x+k...(1)
y=5x-7...(2)


sub (2) to (1):


5x - 7 = 2x^2 - 3x + k


2x^2 - 8x + (k+7) = 0


x = [ 8 √(64 - 8(k+7) ] / 4


x = 2 √ [4 -(k+7)/2]


sub it to (1) :


y = 5{2 √[4 - (k+7)/2]} - 7


y = 3 5 √[4 -(k+7)/2]





2009-04-15 20:51:10 補充：
Q3 ( ± 顯示唔到)

x = [ 8 ± √(64 - 8(k+7) ] / 4

x = 2 ±√ [4 -(k+7)/2]

sub it to (1) :

y = 5 {2 ±√[4 - (k+7)/2]} - 7

y = 3 ± 5 √[4 -(k+7)/2]

1,2題人地都答對左,我唔寫,
第三題唔太難,記住一條算式:b^2-4ac
3.
y=2x^2-3x+k-------1
y=5x-7 -------2
把1代入2
2x^2-3x+k=5x-7
2x^2-8x+k+7=0
a=2,b=-8,c=k+7
用b^2-4ac
(8)^2-4(2)(k+7)=0
64-(8)(k+7)=0
64-8k-56=0
8-8k=0
8=8k
k=1

1.
x=3,y=2

2.
x=6,y=0