# Simultaneous Equations

## System of Equations

## System of Linear Equations

The number of equations should be at least the number of unknowns in order to solve the variables. System of linear equations can be solved by several methods, the most common are the following,

1. Method of substitution

2. Elimination method

3. Cramer's rule

Many of the scientific calculators allowed in board examinations and class room exams are capable of solving system of linear equations of up to three unknowns.

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## Example 01 - Simultaneous Non-Linear Equations of Three Unknowns

**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)

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