x+2y-3z=0,5x-6y+7z=0,则x∶y∶z=____.

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x+2y-3z=0,5x-6y+7z=0,则x∶y∶z=____.
x+2y-3z=0,5x-6y+7z=0,则x∶y∶z=____.

x+2y-3z=0,5x-6y+7z=0,则x∶y∶z=____.
消元~令两个式子为(1)(2)
(1)*3,为3x+6y-9z=0(3),(3)+(2)=8x-2z=0,所以x:z=1:4(5)
(1)*5,为5x+10y-15z=0(4),(4)-(2)=16y-22z=0,所以y:z=11:8(6)
(5)*2=2:8,(6)为y:z=11:8,所以x:y:z=2:11:8

3x+6y-9z=0 3x+6y=9z 6y=5x+7z
代入得3x+5x+7z=9z 8x=2z z=4x
代入得6y=5x+28x=33x y=33z/6
则x:y:z=x:(33/6)x:4x
x:y:z=6:33:24=2:11:8