F.2 聯立二元一次方程

1)
5x + 2y = -3 .....................[1]
2x - 3y = -24 .....................[2]

2x(1) - 5x(2) :
2(5x + 2y) - 5(2x - 3y) = 2(-3) - 5(-24)
19y = 114
y = 6 ................[3]

把 [3] 代入 [1]中:
5x + 2(6) = -3
x = -3

所以 x = -3, y = 6


2a)
4x + 6y = 41 ............ [1]
x + 4y = 19 ........... .. [2]

(1) - 4x (2):
4x + 6y - 4 (x + 4y) = 41 - 4 (19)
-10y = - 35
y = 3.5 .............[3]

把 [3] 代入 [1] 中:
4x + 6 (3.5) = 41
x = 5

所以 x = 5, y = 3.5


2b)
4/a + 6/b = 41, 1/a + 4/b = 19 比較
4x + 6y = 41, x + 4y = 19

設 x = 1/a , y = 1/b, 所以 a = 1/x , b = 1/y
由(a)小題的結果: x = 5, y = 3.5 = 7/2
所以 a = 1/5, b = 2/7

1)
5x + 2y = -3 ...............[1]
2x - 3y = -24 ..............[2]

2x(1) - 5x(2) : 2(5x + 2y) - 5(2x - 3y) = 2(-3) - 5(-24)
19y = 114
y = 6 ...............[3]

代[3]入[1] :

5x + 2(6) = -3
5x=-15
x = -3

所以 x = -3, y = 6
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2a)
4x + 6y = 41 .........[1]
x + 4y = 19 ...........[2]

[2]:x = 19 - 4y..........[3]

代[3]入[1] :

4(19 - 4y) + 6y = 41

76 - 16y + 6y = 41

10y = 35

y = 3.5

y = 3.5代入[2] :

x + 4(3.5) = 19

x = 5

所以x = 5, y = 3.5


2b)
4/a + 6/b = 41, 1/a + 4/b = 19 比較
4x + 6y = 41, x + 4y = 19

設 x = 1/a , y = 1/b, 所以 a = 1/x , b = 1/y
由(a)小題的結果: x = 5, y = 3.5 = 7/2
所以 a = 1/5, b = 2/7

1) 5x + 2y = -3--------(1)
2x - 3y = -24-------(2)
(1) x 3:
15x + 6y = -9------(3)
(2) x 2:
4x - 6y = -48-------(4)
(3) + (4):
19x = -57
x = -3
把x = -3 代入(2):
5(-3) + 2y = -3
-15 + 2y = -3
2y = 12
y = 6
聯立方程的解 x = -3, y = 6.

2a) 4x + 6y = 41---------(1)
x + 4y = 19-----------(2)
從(2), 可得:
x = 19 - 4y------------(3)
把(3)代入(1):
4(19 - 4y) + 6y = 41
76 - 16y + 6y = 41
10y = 35
y = 3.5
把y = 3.5代入(3):
x = 19 - 4(3.5)
= 5

2b) 4/a = 4 x 1/a
6/b = 6 x 1/6
.
.
. (你應該明啦)
so, 1/a= 5
a = 1/5
1/b = 3.5
b = 2/7

THAT'S ALL.

1)
5x + 2y = -3 ---- (1)
2x - 3y = -24 ---- (2)

(1)X 2 = 10x + 4y = -6 --- (3)
(2)X 5 = 10x - 15y = -120 ---(4)

(3)-(4):
10x + 4y = -6
-)10x - 15y = -120
------------------------------
19y = 114
y = 6

把y=6 代入 (1):
5x + 2 (6) = -3
x = -3
所以, x=-3, y=6

2a)
4x + 6y = 41 ----(1)
x + 4y = 19 ----(2)

(2)X4 = 4x + 16y = 76 ----- (3)

(1)-(3):
4x + 6y = 41
-) 4x + 16y = 76
--------------------------
-10y = -35
y = 7/2

把y=7/2 代入 (1):
4x + 6(7/2) = 41
x = 5
所以, x=5, y=7/2

2b)
a=1/x, b=1/y
所以, a=1/5, y=2/7