Example 02 - Simultaneous Non-Linear Equations of Three Unknowns

Multiply the three equations
$(xy)(yz)(xz) = -3(12)(-4)$

$x^2 y^2 z^2 = 144$

$(xyz)^2 = 144$

$xyz = \pm 12$   →   Equation (4)
 

Equation (4) divided by Equation (2)
$\dfrac{xyz}{yz} = \dfrac{\pm 12}{12}$

$x = \pm 1$           answer
 

Equation (4) divided by Equation (3)
$\dfrac{xyz}{xz} = \dfrac{\pm 12}{-4}$

$y = \pm 3$           answer
 

Equation (4) divided by Equation (1)
$\dfrac{xyz}{xy} = \dfrac{\pm 12}{-3}$

$z = \pm 4$           answer