Question

⑤ x+y/3=y+z/4=z+x/5 x+y+z=12 ⑥ x/2=y/3=z/5 2x=2y-z=16

Answer 1

设(x+y)/3=(y+z)/4=(z+x)/5=k
x+y=3k
y+z=4k
x+z=5k
以上3式相加得
2(x+y+z)=12k
x+y+z=6k
x+y+z=12
6k=12
k=2
x+y=3k=3*2=6.1
y+z=4k=4*2=8.2
x+z=5k=5*2=10.3
将1式代入x+y+z=12得
6+z=12
z=6
将2式代入x+y+z=12得
8+x=12
x=4
将3式代入x+y+z=12得
10+y=12
y=2
所以x=4,y=2,z=6
设x/2=y/3=z/5=k
x=2k
y=3k
z=5k
2x+2y-z=16
2*2k+2*3k-5k=16
4k+6k-5k=16
5k=16
k=16/5
x=2k=2*16/5=32/5
y=3k=3*16/5=48/5
z=5k=5/16/5=16