solve an equation
3x+2y=8
2x+3y=7 expressed by direct division is as follows:
3 2 8
2 3 7
The first column times 3 minus the second column times 2:
5 0 10
2 3 7
The first column is divided by 5:
1 0 2
2 3 7
X=2 eliminates an unknown by direct division.
Direct division can also be applied to multivariate equations. In the history of world mathematics, it is very great for ancient mathematicians in China to create direct division to solve equations. It not only effectively represents various multivariate equations as "equations", but also obtains the correct answer to the question through direct division, a universally applicable method. No country in the world solved multivariate equations so completely in that early age. In foreign countries, the method comparable to the "equation skill" in "Nine Chapters of Arithmetic" first appeared in17th century, which was attributed to Leibniz in Germany. In mathematics, Leibniz is one of the founders of calculus, and he has also made important contributions to mathematical logic. 1693, he put forward the theory of multivariate linear equations completely.
China's ancient mathematicians reached the peak of world mathematics development more than once, and made unparalleled achievements in the study of equations at that time, making great contributions to the history of world mathematics and civilization. This is the pride of the Chinese nation. Of course, everything can be divided into two parts. In ancient China, the study of equations was often limited to solving practical problems, and did not pay attention to the study of basic theories, especially the properties of equations. Therefore, there are also shortcomings that cannot be ignored. For example, although China has a negative number, the relationship between the number and degree of the roots of the equation and the relationship between the roots and the coefficients has never been discussed. Even the answers to two adjacent questions in Yi Gu Yuan are just two roots of the same quadratic equation, but neither Liu Yi nor Yang Hui pointed this out. Quaternary method can not be applied to equations with more than four elements; And so on. At that time, these problems needed to be solved by Jia Xian, Qin, Zhu Shijie and others, which was demanding of the ancients, but may be solved in the further development. However, due to the obstruction of the decadent feudal system, the outstanding mathematical achievements in the Song and Yuan Dynasties have not been developed since then, but have been lost for a long time. Coupled with imperialist aggression, China has not yet produced modern science. Until the end of the 18th century and the beginning of the 19th century, Jiao Xun (1763- 1820), Wang lai (1768- 18 13), Li Rui and Luo Shilin (1789). When there is a second sign change, there are two positive roots; When there are three signs, there are three or one positive root; When four symbols change, there are four or two positive roots. This is the same as the so-called "Descartes sign law" (AD 1637). Li Rui also found that the equation has negative roots and multiple roots. However, the above results are later than those obtained by Europeans.