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```				   solve simultaneously:
6(x+y)=5xy
21(y+z)=10yz
14(z+x)=9zx
```

5 years ago

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```										6(x+y) = 5xy      ................1
21(y+z) = 10yz        ...........2
14(z+x) = 9zx   .........3

eq1 = 6(x+y) = 5xy
1/x + 1/y = 5/6      ...............4

eq2 = 21(y+z) = 10yz
1/y + 1/z = 10/21       ................5

eq3 = 14(z+x) = 9zx
1/z+1/x = 9/14      ...............6

eq 5 + eq 6 - eq 4
2/z = 10/21 + 9/14 - 5/6
z = 7
x = 2
y = 3

```
5 years ago
```										6(x+y)=5xy
21(y+z)=10yz
14(z+x)=9zx
6x + 6y = 5xy ----------------------------------(i)
21y + 21z = 10yz --------------------------------------(ii)
14z + 14x = 9zx --------------------------------------------------(iii)
dividing (i) by xy we get
1/y + 1/x = 5/6 -------------------------------(iv)
dividing (ii) by yz we get
1/z + 1/y = 10/21 ----------------------------------(v)
dividing (iii) by zx we get
1/x + 1/z = 9/14 --------------------------------------(vi)

subtracting (vi) from (v)
1/y - 1/x = 10/21 - 9/14 = -1/6 ---------------------- (vii)
2/y = 5/6 - 1/6 = 4/6 = 2/3
1/y = 1/3
==> y=3 -----------------------------------------------(A)
substituting the value of (A) in (v) we get :
1/z = 10/21 - 1/3 =1/7
==> z=7 -----------------------------------------------(B)
substituting the value of (B) in (vi) we get :
1/x = 9/14 - 1/7 = 1/2
==> x = 2 ------------------------------------------------(C)
----------------------------------|
x = 2 ----------------- from (C)   |
y = 3 ----------------- from (A)   |
z = 7 ----------------- from (B)   |
----------------------------------|

```
5 years ago

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