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indrayani bargaje Grade: 10
        solve simultaneously:

6(x+y)=5xy
21(y+z)=10yz
14(z+x)=9zx
6 years ago

Answers : (2)

vikas askiitian expert
510 Points
										

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


 

6 years ago
Sudheesh Singanamalla
114 Points
										

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)


Adding (iv) and (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)


so the answers are


----------------------------------|


x = 2 ----------------- from (C)   |


y = 3 ----------------- from (A)   |


z = 7 ----------------- from (B)   |


----------------------------------|





6 years ago
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