<明日交`40 m> F.2 二元一次方程 (1)

其實好簡單:
Let 1/a be x,1/b be y..........(a)

4x-6y=21........(1)
9x+5y=1.........(2)

From(1):
4x=21+6y
x=(21+6y)/4..........(3)

Sub(3) into (2):
9(21+6y)/4+5y=1
(189+54y+20y)/4=1
(189+74y)/4=1
189+74y=4
74y=4-189
74y=-185
y=-2.5

Sub y=2.5 into (1):
4x+15=21
4x=6
x=4/6
x=2/3

From (a):
x=2/3=1/a
a=3/2
y=-2.5=1/b
-5/2=1/b
b=-2/5

Let x = 1/a & y = 1/b.
(i.e. a = 1/x & b = 1/y)

Then, the equations will be changed to :
4x - 6y = 21 ---------- (1)
9x + 5y = 1 ---------- (2)

From (1) : x = 21/4 + (3/2)y ---------- (3)
Sub. (3) into (2) :
9[21/4 + (3/2)y] + 5y = 1
189/4 + (27/2)y +5y = 1
__________(37/2)y = - 185/4
______________y = - 5/2 ---------- (4)

Sub. (4) into (3) : x = 21/4 + (3/2) (- 5/2) ==> x = 3/2

So, a = 1/x = 2/3 & b = 1/y = - 2/5.