二元一次方程组A1x+B1y=C1 A2x+B2y=C2的解

2024-11-24 12:10:21
推荐回答(2个)
回答1:

一式*A2
A1*A2x+B1*A2y=C1*A2 (2)
二式*A1
A2*A1x+B2*A1y=C2*A1 (3)
(2)-(3):
y=(C1A2-C2A1)/(B1A2-B2A1)

一式*B2
A1*B2x+B1*B2y=C1*B2 (4)
二式*B1
A2*B1x+B2*B1y=C2*B1 (5)
(4)-(5):
x=(C1B2-C2B1)/(A1B2-A2B1)
所以,方程组的解为:

x=(C1B2-C2B1)/(A1B2-A2B1)
y=(C1A2-C2A1)/(B1A2-B2A1)

回答2:

这道题真麻烦!

由A1x+B1y=C1, 得到 x=(C1/A1)-(B1/A1)y, 代入A2x+B2y=C2中,求得

y=[C2-A2C1/A1]/[B2-A2B1/A1],再代入x=(C1/A1)-(B1/A1)y中,求得

x=(C1/A1)-(B1/A1)[C2-A2C1/A1]/[B2-A2B1/A1]