請將以下的題目用加減消元法來解決

2009-02-07 11:39 pm
1.{2a-7b=0
{4a-7b+10=0
2.{9p+4q+2=0
{9p-2q-28=0
3.{3x+4y=2
{6x-7y=19

回答 (2)

2009-02-08 3:42 am
✔ 最佳答案
{  2a - 7b = 0 -------(1)
{4a - 7b + 10 = 0 -------(2)

(2) - (1)
4a - 7b +10 - ( 2a - 7b ) = 0 - 0
 4a - 7b + 10 - 2a + 7b = 0
       2a + 10 = 0
         a = -5

將 a = -5 代入 (1)
2 (-5) - 7b = 0
 -10 - 7b = 0
   -7b = 10
    b = - ( 10 / 7 )

∴a = -5,b = - ( 10 / 7 )。

==========================

{9p + 4q + 2 = 0 -------(1)
{9p - 2q - 28 = 0 -------(2)

(1) - (2)

9p + 4q + 2 - ( 9p - 2q - 28 ) = 0
 9p + 4q + 2 - 9p + 2q + 28 = 0
         6q + 30 = 0
           q = -5

將 q = -5 代入 (1)
9p + 4(-5) + 2 = 0
 9p - 20 + 2 = 0
     9p = 18
     p = 2

∴p = 2,q = -5。

==========================

{3x + 4y = 2 --------(1)
{6x - 7y = 19 --------(2)

(1) × 2 - (2)
2 ( 3x + 4y ) - ( 6x - 7y ) = 2 × 2 - 19
   6x + 8y - 6x + 7y = -15
         15y = -15
          y = -1

將 y = -1 代入 (1)
3x + 4(-1) = 2
  3x - 4 = 2
   3x = 6
    x = 2

∴x = 2,y = -1。
2009-02-08 12:20 am
上面的方程叫a,下面叫b
1.將a乘2,再減b
4a-14b-4a+7b-10=0

7b-10=0,
b=7分之10,a=5

2.將a減b
9p+4q+2-9p+2q+28=0
6q=-30
q=-5,p=2

3.將b減(a乘2)
6x-7y-6x-8y=19-2
-15y=17
y=負十五分之十七x=45分之98
參考: 自己


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