system of equations with 3 variables in denominator I'm having problems with this system of equations: 3/(x+y)+2/(x-z)=3/2 1/(x+y)-(10)/(y-z)=(7)/(3) 3/(x-z)+5/(y-z)=-1/4 I've tried substitution method but that took me nowhere, I'm not sure I can solve it and would appreciate if anyone showed me the proper method to solve this problem.

drobtinicnu 2022-09-13 Answered
system of equations with 3 variables in denominator
I'm having problems with this system of equations:
3 x + y + 2 x z = 3 2
1 x + y 10 y z = 7 3
3 x z + 5 y z = 1 4
I've tried substitution method but that took me nowhere, I'm not sure I can solve it and would appreciate if anyone showed me the proper method to solve this problem.
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Answers (1)

Aydin Rodgers
Answered 2022-09-14 Author has 12 answers
I hope you mean the following.
3 x + y + 2 x z = 3 2 ,
1 x + y 10 y z = 7 3 ,
3 x z + 5 y z = 1 4 .
If so, let 1 x + y = c, 1 x z = b and 1 y z = a
Thus,
3 c + 2 b = 3 2 ,
c 10 a = 7 3
and
3 b + 5 a = 1 4 .
The last two equations give
6 b + c = 11 6 ,
which with first gives
c = 1 3 ,
b = 1 4
and from here we'll get
a = 1 5 .
Thus,
x + y = 3 ,
x z = 4
and
y z = 5 ,
which gives
( x , y , z ) = ( 6 , 3 , 2 ) .

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