f.2 maths(解方程)10分！

1(a)(i)
2x+3y=13 <-----(1)
3x-y=3<-------(2)
From (2) , 3x-y=3
y=3x-3<-------(3)
Sub (3) into (1),
2x+3(3x-3)=13
2x+9x-9=13
11x=22
x=2
Sub x=2 into (3),
y=3(2)-3
y=3

Therefore , x=2 and y=3.

(ii)
2(a+b) +3(a-b) = 13
3(a+b) - (a-b) = 3

Let x=a+b and y=a-b.
Then
2x+3y =13
3x-y=3
From (a)(i),
x=2 and y=3.
Therefore
a+b=2<-----(4)
a-b=3<----(5)
From (4) , a+b=2
b=2-a<-------(6)
Sub (6)into (5),
a-(2-a)=3
a-2+a=3
2a=5
a=5/2
Sub a=5/2 into (6),
b=2-(5/2)
b=-1/2
Therefore , a=5/2 and b=-1/2


(iii)
2/m + 3/n =13
3/m - 1/n = 3
Let x=1/m and y=1/n.
Then
2x+3y=13
3x-y=3

From (a)(i) , x=2 and y=3.
Therefore
2=1/m
3=1/n

By solving the two equations above ,
m=1/2 and n=1/3.

1(a) (i) 2x + 3y = 13
3y = 13 - 2x
y = (13-2x) / 3

Put y into 3x-y=3
3x - (13-2x)/3 =3
9x - (13-2x) = 9
9x - 13 + 2x = 9
9x + 2x = 9 +13
11x = 22
x=2

y = (13-2x)/3
y = [13-2(2)] /3
y = 9/3 = 3

(a) (ii) Let x = (a+b) & y = (a-b)
==> 2x + 3y =13
==> 3x - y =3 (我估你打錯 formula)
By result of (a) (i) x = (a+b) = 2
y = (a-b) = 3
a+b =2 , a= 2-b
a-b = 3 , (2-b) - b = 3
2- 2b =3
-2b = 1
b = -1/2
a = 2-b
a= 2- (-1/2)
a = 2. 1/2

(a) (iii) Let x = 1/m , y = 1/n
==> 2x + 3y =13
==> 3x - y =3

By result of (a) (i) x = 1/m = 2 ; m = 1/2
y = 1/n = 3 ; n = 1/3

先將 3x-y=3
=> 3x - 3 = y
put into
2x + 3y = 13
=> 2x + 3(3x -3) =13
=> 2x + 9x - 9 =13
=> 11x = 13 + 9
=> x = 2

跟住將 x = 2 put into either first or second formula
自然計到 y = 3

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2007-05-28 13:29:01 補充：
a b = x = a b = 2a - b = y = a - b = 3