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Understanding linear conversion equations is essential when we want to translate values from one measurement system to another. In our case, we aim to convert temperatures between a known scale, Celsius, and an unknown 'Strange' scale.

A linear conversion equation is, at its core, a simple linear equation of the form: \( y = mx + b \), where \( y \) represents the value in the new scale, \( x\) is the value in the original scale, \( m\) is the slope of the line (also known as the rate of conversion), and \( b\) is the y-intercept (the value of \( y\) when \( x = 0\)).

In the context of temperature conversion, the slope \( m\) tells us how much the temperature on one scale changes for a one-degree change on the other scale. The y-intercept \( b\) indicates the value on one scale when the temperature on the other scale is zero. By figuring out these constants, \( m\) and \( b\), we can move back and forth between the Strange and Celsius scales.

The Celsius scale, also known as centigrade, is a temperature scale based on the boiling and freezing points of water, which are precisely defined as 100°C and 0°C respectively, at sea level and standard atmospheric pressure.

It's a widely adopted scale that is used for everyday temperature measurements in most of the world, except for a few countries that use the Fahrenheit scale. When performing conversions between temperature scales, understanding the reference points of the Celsius scale is crucial, as they often serve as the foundation for creating conversion equations such as the one needed to translate temperatures to and from the Strange scale.

Additionally, the Celsius scale has a direct relationship with the Kelvin scale used in scientific measurements, with the formula \( K = C + 273.15 \) to switch between them.

A system of linear equations consists of two or more linear equations with the same set of variables, which we aim to solve simultaneously. For temperature scale conversion, we establish a system based on known reference points that correspond to the same physical temperatures across scales. In this problem, we identify the freezing and boiling points of water on both scales and express these as linear equations.

To solve the system, various methods can be used, such as substitution, graphing, or elimination. The elimination method often proves efficient when the system is simple and involves two equations and two variables, as it allows for the quick elimination of a variable by adding or subtracting the equations. By manipulating the equations, we solve for one variable at a time, ultimately obtaining the values needed for the linear conversion equation ('m' and 'b').

Understanding the concept of systems of linear equations and being fluent in solving them is a valuable skill, not only for converting temperatures but also for various scientific and mathematical applications.