# system of non-linear equations

## 02 - Solution to Equations Involving Variable Exponent

Solve for the value of x from each of the following equations:

- 9
^{x}- 6(9^{-x}) - 1 = 0 - 2
^{x + 1}· 3^{x}= 5^{x + 3}

## 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)

## Example 06 - Simultaneous Non-Linear Equations of Two Unknowns

**Problem**

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

$x^2y + y = 17$ ← Equation (1)

$x^4y^2 + y^2 = 257$ ← Equation (2)

## Example 05 - Simultaneous Non-Linear Equations of Two Unknowns

**Problem**

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

$x + 2y = 6$ ← Equation (1)

$\sqrt{x} + \sqrt{y} = 3$ ← Equation (2)