Answer:
z = -12
Step-by-step explanation:
Rewritting the equations, we have:
x + y = xy (eq1)
2x + 2z = xz (eq2)
3y + 3z = yz (eq3)
From the first equation:
x = y/(y-1) (eq4)
From the third equation:
y = 3z/(z - 3) (eq5)
Using the value of y from (eq5) in (eq4), we have:
x = [3z/(z - 3)] / [3z/(z - 3) - 1]
x = [3z/(z - 3)] / [(3z - z + 3)/(z - 3)]
x = 3z / (2z + 3) (eq6)
Using the value of x from (eq6) in (eq2), we have:
6z / (2z + 3) + 2z = (3z / (2z + 3))*z
(6z + 4z^2 + 6z) / (2z + 3) = 3z^2 / (2z + 3)
12z + 4z^2 = 3z^2
z^2 = -12z
z = -12
