**Problem**

今有共買物，人出八，盈三；人出七，不足四。問：人數、物價各幾何？

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?

**Solution**

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.

**Excess:**

**Deficit:**