Example 07 - Simultaneous Non-Linear Equations of Two Unknowns

Multiply Equation (1) by 3
$\dfrac{9}{x^2} - \dfrac{12}{y^2} = 6$   ←   Equation (3)
 

Multiply Equation (2) by 4
$\dfrac{20}{x^2} - \dfrac{12}{y^2} = 17$   ←   Equation (2)
 

Subtract Equation (3) from Equation (4)
$\dfrac{11}{x^2} = 11$

$x^2 = 1$

$x = \pm 1$
 

Substitute x = ±1 to Equation (1)
$3 - \dfrac{4}{y^2} = 2$

$1 = \dfrac{4}{y^2}$

$y^2 = 4$

$y = \pm 2$
 

The solutions are
(1, 2), (1, -2), (-1, 2), and (-1, -2)           answer