Solving 2 equations with 3 unknowns

Question

Can please someone help me solve this puzzle, I want to find the right : x,y and z

here's my equations:

• (1+x*0.005556)*y-1=0
• (1.023895)*z-y=0

with (x,y,z)>0

Answer 1

$$\begin{align}(1+0.005556x)y-1=0&\implies x = \frac{\frac1y - 1}{0.005556}\tag{1}\\1.023895z-y=0&\implies z = \frac{y}{1.023895}\tag{2}\end{align}$$

From $(1)$, we have that $x > 0 \forall y\in(0, 1)$. From $(2)$, we have that $z > 0\forall y > 0$. Therefore, $x, y, z> 0\forall y\in(0, 1)$.