1. ## Substitution question

When doing substitution to solve a system of equations, how can i tell if it has one solution, no solution, or infinitely many solutions.

2. Originally Posted by campvoorhees23146
When doing substitution to solve a system of equations, how can i tell if it has one solution, no solution, or infinitely many solutions.
Hi campvoorhees23146,

If the slopes of the two equations are equal, then there is no solution.

If one equation is a multiple of the other equation, then there are infinitely many solutions.

3. Originally Posted by campvoorhees23146
When doing substitution to solve a system of equations, how can i tell if it has one solution, no solution, or infinitely many solutions.
Poor Man's Definitions:

1) If you get one, there is one. Example x = 3
2) If you get nonsense, there is none. Example 3 = 7
3) If you get "duh", there are many. Example 12 = 12

4. Originally Posted by TKHunny
Poor Man's Definitions:

1) If you get one, there is one. Example x = 3
2) If you get nonsense, there is none. Example 3 = 7
3) If you get "duh", there are many. Example 12 = 12
LOL