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The procedure referred to by the term ''fangcheng'' and explained in the eighth chapter of The Nine Chapters, is essentially a procedure to find the solution of systems of ''n'' equations in ''n'' unknowns and is equivalent to certain similar procedures in modern [[linear algebra]]. The earliest recorded ''fangcheng'' procedure is similar to what we now call [[Gaussian elimination]].
The ''fangcheng'' procedure was popular in ancient China and was transmitted to [[Japan]]. It is possible that this procedure was transmitted to [[Europe]] also and served as precursors of the modern theory of [[Matrix (mathematics)|matrices]], [[Gaussian elimination]], and [[determinant]]s.<ref name="Hart02"/> It is well known that there was not much work on linear algebra in [[Greece]] or [[Europe]] prior to [[Gottfried Leibniz]]'s studies of [[Elimination theory|elimination]] and determinants, beginning in 1678. Moreover, Leibniz was a [[Sinophile]] and was interested in the translations of such Chinese texts as were available to him.<ref name="Hart02">{{cite book |author=Roger Hart|title=The Chinese Roots of Linear Algebra |date=2011 |publisher=The Johns Hopkins University Press |url=https://muse.jhu.edu/chapter/322679 |accessdate=6 December 2016}}</ref>
==On the meaning of ''fangcheng''==
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** 1 bundles of high-quality rice straw, 2 bundles of mid-quality rice straws and 3 bundle of low-quality rice straws produce 26 units of rice
** Question: how many units of rice can high, mid and low quality rice straw produce respectively?
* Solution:
** High-quality rice straw each produces 9 + 1/4 units of rice
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There is also a special procedure, called "procedure for positive and negative numbers" (''zheng fu shu'') for handling negative numbers. This procedure is explained as part of the method for solving Problem 3.
===On Problem 13===
In the collection of these 18 problems Problem 13 is very special. In it there are 6 unknowns but only 5 equations and so Problem 13 is indeterminate and does not have a unique solution. This is the earliest known reference to a system of linear equations in which the number of unknowns exceeds the number of equations. As per a suggestion of Jean-Claude Martzloff, a historian of Chinese mathematics, Roger Hart has named this problem "the well problem."
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