Writing Project 10:

Number of variables versus number of equations

Explain, reasoning with the substitution method, why we usually get only one single solution if we have a system of 3 linear equations with 3 variables. Clearly describe why this is not the case in the following two examples:

Example 1:

Example 2:

2x + 3y - 5w = 2

3x - 2y + 2w = 3

8x - y - w = 8

x + 2y = 2

5x - 4z = -4

2x - y - 2z = 1

Erich Prisner, August 2003