✔ 最佳答案
(1) 解方程組
x + y = 74 -------(1)
x + z = 53 -------(2)
y + z = 109 ------(3)
解:
(1) + (2) + (3),得:
2x + 2y + 2z = 236
x + y + z = 118 ---(4)
(4) - (1),得:
z = 44
(4) - (2),得:
y = 65
(4) - (3),得:
x = 9
所以x = 9, y = 65, z = 44.
(2) 解方程組
x - y - z = 5 ------(1)
x + y = 20 -------(2)
yz = 7 -------------(3)
解:
(2) - (1),得:
2y + z = 15
z = 15 - 2y ------(4)
把(4)代入(3),得:
y (15 - 2y) = 7
2y² - 15y + 7 = 0
(2y - 1)(y - 7) = 0
y1 = 1/2, y2 = 7
當y1 = 1/2時,x1 = 20 - 1/2 = 39/2, z1 = 7/(1/2) = 14
當y2 = 7時,x2 = 20 - 7 = 13, z2 = 7/7 = 1
(3) 解方程組
x = 3 - y ------(1)
y = 3 - z -------(2)
x - z = y -------(3)
解:把(2)代入(1),得:
x = 3 - (3-z)
x = z -----------(4)
把(2)代入(3),得:
x - z = 3 - z
x = 3
從而z = 3, y = 3 - 3 = 0.
所以x = 3, y = 0, z = 3.