# Example 07 - Simultaneous Non-Linear Equations of Two Unknowns

**Problem**

Solve for $x$ and $y$ from the given system of equations.

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

$\dfrac{5}{x^2} - \dfrac{3}{y^2} = \dfrac{17}{4}$ ← Equation (2)

**Solution**

Multiply Equation (1) by 3

$\dfrac{9}{x^2} - \dfrac{12}{y^2} = 6$ ← Equation (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*