Please see the attached file.
Suppose you need to find numbers x, y, and z such that the following three equations are all simultaneously true:
2x + y − z = 8,
− 3x − y + 2z = − 11,
− 2x + y + 2z = − 3
This is called a system of linear equations for the unknowns x, y, and z. They are called linear because each term is either constant or is a constant times a single variable to the first power. The goal is to transform this system to an equivalent one so that we can easily read off the solution. The operations to transform a system of equations to another, whilst still preserving the solutions are as follows:
? multiply or divide a row by a non-zero number
? switch two rows
? add or subtract a (not necessarily integer) multiple of one row to another one
The strategy is as follows: eliminate x from all but the first equation, eliminate y from all but the second equation, and then ...
The solution provides detailed theory for the problem in a 3-page Word document.