## 10.8.3 Number of solutions to a system.

Consider the system of equations:

$3x + 2y = 16$

$y = -\frac32 x + 8$

One solution for both of these equations is at (2,5).  However, there is another solution at (0,8).  Since the solution is represented by the point of intersection, how is it possible for 2 lines to intersect at more than 1 place?

Resources:

• Notes: Number of solutions

Assignment

• p455 #1-3, 5-7, 9, 12-17 *18-20

Things you should know after today:

• how to determine the number of solutions given the graphs of a system
• the relationship between number of solutions and the slopes and y-intercepts of the lines in a system
• how to determine the number of solutions by inspection of the system