解聯立方程

2x + y = 7 ...... [1]
xy = 6 ...... [2]

From[1] :
y = 7 - 2x ...... [3]

Put [3] into [2] :
x(7 - 2x) = 6
7x - 2x² = 6
2x² - 7x - 6 = 0
(2x - 3)(x - 2) = 0
x = 3/2 or x = 2

When x = 3/2, put x = 3/2 into [1] :
2(3/2) + y = 7
3 + y = 7
y = 4

When x = 2, put x = 2 into [1] :
2(2) + y = 7
4 + y = 7
y = 3

Hence, x = 3/2, y = 4
or x = 2, y = 4

2x + y = 7
2xy + y^2 = 7y
2*6 + y^2 = 7y
y^2 - 7y + 12 = 0
( y - 3 )( y - 4 ) = 0
y = 3 or 4

當 y = 3, x = 2 ;
當 y = 4, x = 3/2 .

所以 (x,y) = (2,3) 或 (3/2,4) .

2x+y=7 i
xy=6 ii
由i,y=7-2x iii
代iii入ii
7x-2x^2=6
x=3/2 或x=2
代x=3/2入iii
y=7-2(3/2)
y=4
代x=2入iii
y=7-2*2
y=3
(x,y)=(3/2,4)
(x,y)=(2,3)