1. Linear Systems
Note / Handout

2. Definitions A linear system is simply two or more lines (equations).
To solve a linear system means to find the point of intersection.
What is a point of intersection?
It is where the lines meet.

3. Solve each linear system graphically.
y = -2x+1 y = x – 5
y = 2x x + y = 3
x + y = 0 3x + y = -4

4. Solve the system algebraically!
y = 2x
x + y = 3

5. Word Problem Example Two companies rent trucks.
Company A charges $80.00 for the truck, plus $0.20 / km.
Company B charges $0.60/km
a) Write an equation for each company’s rental cost in terms of distance driven.

6. Word Problem Continued
b. Graph both equations on the same axes and find the point of intersection.
c. Explain the meaning of the point of intersection.
d. Which company is cheaper if you drive 150km? or 250km?