已知:方程组{ax+3b=c,2ax-by=5c 的解是{x=1,y=-1,则a:b:c=______:______:______.

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已知:方程组{ax+3b=c,2ax-by=5c 的解是{x=1,y=-1,则a:b:c=______:______:______.

已知:方程组{ax+3b=c,2ax-by=5c 的解是{x=1,y=-1,则a:b:c=______:______:______.
已知:方程组{ax+3b=c,2ax-by=5c 的解是{x=1,y=-1,则a:b:c=______:______:______.

已知:方程组{ax+3b=c,2ax-by=5c 的解是{x=1,y=-1,则a:b:c=______:______:______.
ax+3b=c,2ax-by=5c
x=1,y=-1
a+3b-c=0 ①
2a+b-5c=0 ②
由①得
a=c-3b
b=(c-a)/3
c=a+3b
由2得
a=(5c-2b)/2
b=5c-2a
c=(2a+b)/5
a=c-3b=(5c-2b)/2
b=(c-a)/3=5c-2a
c=a+3b=(2a+b)/5
化简
14c=5a
3c=-5b
3a=-14b

b=-3a/14
c=-5b/3=5a/14
a:b:c=a:-3a/14:5a/14=14:-3:5

x=1,y=-1代入,得
a+3b=c
2a+b=5c
解得a=14/5 c
b=-3/5 c
所以
a:b:c=___14___:___-3___:___5___.