05 - Simultaneous Non-Linear Equations of Three Unknowns Jhun Vert Fri, 04/17/2020 - 04:40 pm

Problem
Solve for x, y, and z from the following simultaneous equations.
 

$x^2 - yz = 3$   ←   Equation (1)

$y^2 - xz = 4$   ←   Equation (2)

$z^2 - xy = 5$   ←   Equation (3)
 

01 - Simultaneous Non-Linear Equations of Three Unknowns Jhun Vert Fri, 04/17/2020 - 04:31 pm

Problem
Solve for x, y, and z from the following simultaneous equations.
 

$z^x \, z^y = 100\,000$   ←   equation (1)

$(z^x)^y = 100\,000$   ←   equation (2)

$\dfrac{z^x}{z^y} = 10$   ←   equation (3)