Suppose there is an item bought in common. If each person pays 8 coins, there is an excess of 3 coins; if each person pays 7 coins, there is a deficiency of 4 coins. Question: What is the number of people, and what is the price of the item?
Let be the number of people, and the price of the items in coins.
Write the problem as a system of linear equations:
Use Cramer's rule
There are 7 people, and the items cost 53 coins.
Note: The method employed in the Jiuzhang Suanshu is actually the method of Double False-Position, which turns out to be equivalent to Cramer's rule for 2 x 2 systems of linear equations.