Simultaneous equations

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Simultaneous equations are finite sets of mathematical equations where the solution to the set of equations solves each individual equation. There are many different types of simultaneous equations, such as linear simultaneous equations and differential simultaneous equations. Sometimes there may be more than one solution for each variable and sometimes there may be no solution.

Linear Simultaneous Equation

For a more detailed treatment, see Linear equations.
The most simple type of simultaneous equations are linear. These are algebraic equations (they contain no derivatives) and linear as they only contain terms of the form ax, where a is a constant and x is one of the variables (no exponentials or sines etc.). An example of a system of linear equations is:

They are the simplest type of simultaneous equation to solve and be solved using Gaussian elimination

See also