The value of X is 1/3 and Y is 1/2 and Z is 1/4.
According to the statement we have given the equations which are
X + Y = 5XY -(1)
Y + Z = 6YZ -(2)
Z + X = 7XZ -(3)
and we have to find the value of X,Y,Z.
So, solve the equations for the X,Y,Z
From (1) equation
Y = X / (5X-1) -(4)
From (3) equation
Z = X / (7X-1) -(5)
Put (4) and (5) in (2) then
X / (5X-1) + X / (7X-1) = 6{[X / (5X-1)][X / (7X-1)]}
X(7X-1) + X(5X-1) = 6{[X / (5X-1)][X / (7X-1)]} / {[1 / (5X-1)][1 / (7X-1)]}
Then after solving
12(X)^2 -2X = 6(X)^2
6(X)^2 -2X = 0
X (6X-2) = 0
X = 0, X = 1/3
Here X = 0 is neglected.
So, X=1/3 -(6)
Put (6) in (4) and (5) then
From 4
Y = X / (5X-1)
Y = (1/3) / (5(1/3)-1)
Y = (1/3) / (2/3)
Y = 1/2.
From (5) equation
Z = X / (7X-1)
Z = (1/3) / (7(1/3)-1)
Z = (1/3) / (4/3)
Z = 1/4.
So, The value of X is 1/3 and Y is 1/2 and Z is 1/4.
Learn more about SUBSTITUTION METHOD here https://brainly.com/question/22340165
#SPJ1
