On China's ancient linear equations, China's ancient linear equations, China's ancient linear equations, China's ancient linear equations and China's ancient linear equations, the research started very early in China, and many achievements were included in the ancient mathematics book Nine Chapters Arithmetic (introduced in the first volume of this book). One of the nine chapters of arithmetic is "Equation". The first question in this chapter is translated into modern Chinese as follows: 3 bundles of superior grains, 2 bundles of middle grains, 1 bundles of equal grains, and * * * is 39 buckets (the volume commonly used in rural areas in the past was unit of volume); 2 bundles of excellent grain, 3 bundles of medium grain, 1 bundle of poor grain, * * * is 34 buckets; Upper valley 1 bundle, 2 bundles in middle valley, 3 bundles in lower valley, * * is 26 buckets. Find out how many barrels there are in each bundle of the upper, middle and lower valleys. The equations shown in the figure below are listed in the book. In ancient China, equations were listed by calculation (see the colorful pages in front of this book). The above problems are expressed in modern mathematical language, which is equivalent to setting X buckets in each bundle of Yougu. What is shown in the home page of ternary linear equations is actually the coefficient of each equation and the corresponding constant term. In ancient times, when solving equations, calculation tools were also used. The specific solution is equivalent to the addition, subtraction and elimination methods we are learning now. In the first textbook of Algebra (I), we have already introduced that China used negative numbers very early, and a typical example of negative numbers is in the "Equation" chapter of "Nine Chapters of Arithmetic". "More money" is positive and "less money" is negative; And so on. The problem of insufficient subtraction may occur when solving equations, so our ancestors used "addition and subtraction" to solve it, which is equivalent to the addition and subtraction of positive and negative numbers we have learned (for examples of using positive and negative numbers and "addition and subtraction", please refer to the fourth question in Group 5 B of this chapter). Compared with Europe, our ancestors can be said to have mastered the solution of the above linear equations more than 1000 years ago.