數學[解以下有三個未知數的聯立方程]20分！

From (1),
a = 4-b-c .....................(4)
sub (4) into (2)
2(4-b-c)-b+c = 0
8-3b-c = 0
c=8-3b...............(5)

sub (4) into (3)
2(4-b-c)+b-3c = 10
8-b-5c = 10
-b-5c = 2.....................(6)

sub (5) into(6)
-b-5(8-3b) = 2
-b-40+15b = 2
14b = 42
b = 3

put b = 3 into (5)
c = 8-3(3)
c= -1

put b=3,c=-1 into (4)
a = 4-3-(-1)
a = 2

(3)-(2)
2b-4c=10
b-2c=5
b=2c+5 --------(4)
Put (4) into (1)
a+3c+5=4
a=-3c-1 ---------(5)
Put (5),(4) into (3)
2(-3c-1)+2c+5-3c=10
c=-1 ------(6)
Put (6) into (4)
b=-2+5=3
Put (6) into (5)
a=3-1=2

{a+b+c=4...................(1)
{2a-b+c=0..................(2)
{2a+b-3c=10................(3)

(1) + (2)：
3a + 2c = 4.......................(4)

(2) + (3)：
4a - 2c = 10......................(5)

(4) + (5)
7a = 14
a = 2.................................(6)

將(6)代入(4)：
3(2) + 2c = 4
6 + 2c = 4
2c = -2
c = -1...............................(7)

最後，將(6)、(7)代入(1)：
(2) + (-1) + c = 4
1 + c = 4
c = 3

所以：
a = 2
b = -1
c = 3

2009-08-28 15:56:45 補充：
最後打錯了：

應該係...


最後，將(6)、(7)代入(1)：

(2) + b + (-1) = 4

1 + b = 4

b = 3



所以：

a = 2

b = 3

c = -1