Question

求助，数学题

已知3x+4y/2=6x+5y/3=4x-y+13z 求x+2y+z/2x+3y-z

Answer 1

令(3x+4y)/2=(6x+5y)/3=4x-y+13z=k
3x+4y=2k..............1
6x+5y=3k...............2
4x-y+13z=k............3

1式+2式得
9(x+y)=5k
x+y=5k/9............4
将4式代入1式得
3x+4y=3(x+y)+y=2k
3*5k/9+y=2k
5k/3+y=2k
y=k/3.........5

将5式代入4式得
x+y=5k/9
x+k/3=5k/9
x=2k/9..........6

将5式,6式代入3式得
4x-y+13z=k
4*2k/9-k/3+13z=k
5k/9+13z=k
13z=4k/9
z=4k/117

(x+2y+z)/(2x+3y-z)
=[(x+y)+y+z]/[2(x+y)+y-z]
=[5k/9+k/3+4k/117]/[2*5k/9+k/3-4k/117]
=[8k/9+4k/117]/[13k/9-4k/117]
=[8k*13/117+4k/117]/[13k*13/117-4k/117]
=[108k/117]/[165k/117]
=108/165
=36/55

Answer 2

令(3x+4y)/2=(6x+5y)/3=4x-y+13z=k
3x+4y=2k..............1
6x+5y=3k...............2
4x-y+13z=k............3

1式+2式得
9(x+y)=5k
x+y=5k/9............4
将4式代入1式得
3x+4y=3(x+y)+y=2k
3*5k/9+y=2k
5k/3+y=2k
y=k/3.........5

将5式代入4式得
x+y=5k/9
x+k/3=5k/9
x=2k/9..........6

将5式,6式代入3式得
4x-y+13z=k
4*2k/9-k/3+13z=k
5k/9+13z=k
13z=4k/9
z=4k/117

(x+2y+z)/(2x+3y-z)
=[(x+y)+y+z]/[2(x+y)+y-z]
=[5k/9+k/3+4k/117]/[2*5k/9+k/3-4k/117]
=[8k/9+4k/117]/[13k/9-4k/117]

=[108k/117]/[165k/117]
=108/165
=36/55

Answer 3

令(3x+4y)/2=(6x+5y)/3=4x-y+13z=k
3x+4y=2k..............1
6x+5y=3k...............2
4x-y+13z=k............3

1式+2式得
9(x+y)=5k
x+y=5k/9............4
将4式代入1式得
3x+4y=3(x+y)+y=2k
3*5k/9+y=2k
5k/3+y=2k
y=k/3.........5

将5式代入4式得
x+y=5k/9
x+k/3=5k/9
x=2k/9..........6

将5式,6式代入3式得
4x-y+13z=k
4*2k/9-k/3+13z=k
5k/9+13z=k
13z=4k/9
z=4k/117

(x+2y+z)/(2x+3y-z)
=[(x+y)+y+z]/[2(x+y)+y-z]
=[5k/9+k/3+4k/117]/[2*5k/9+k/3-4k/117]
=[8k/9+4k/117]/[13k/9-4k/117]

=[108k/117]/[165k/117]
=108/165
=36/55

Answer 4

3x+4y/2=4x-y+13z化简为-x+4y/2+y=13z,同时6x+5y/3=4x-y+13z化简为2x+7y/3=13z，列出一个关于x,y的方程组，用含有z的代数式表示出x,y，最后带入所求代数式即可。

Answer 5

看楼主和回复，有些诧异，不知楼主的意思是3x+4y/2？还是(3x+4y)/2？
有点乱！！！