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Method of successive substitution
In [[modular arithmetic]], the '''method of successive substitution''' is a method of solving problems of [[simultaneous congruences]] by using the definition of the congruence equation.

For example, consider the simple set of simultaneous congruences
: ''x'' &equiv; 3 (mod 4)
: ''x'' &equiv; 5 (mod 6)

(contracted; show full)* write the first equation in its equivalent form
* substitute it into the next 
** simplify, use the [[multiplicative inverse]] if necessary
* continue until the last equation
* back substitute, then simplify
* rewrite back in the congruence form


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If the moduli are [[coprime]], the [[chinese remainder theorem]] gives a straightforward formula to obtain the solution.

== See also ==
* [[simultaneous equations]]
[[Category:Modular arithmetic]]