1. Chapter 3 – Linear Systems

2. Solving Systems Using Tables and Graphs
Section 3.1

3. System of Equations
A set of 2 or more equations with the same variables
Ex: −3𝑥+2𝑦= 𝑥+2𝑦=−8

4. Solution of a System
A set of values for variables that makes ALL the equations true.
Ex: −3𝑥+2𝑦= 𝑥+2𝑦=−8
Is −4, −2 a solution to the above system?

5. Using a Graph to Find a Solution
1. Ex: 𝑦=2𝑥−1 𝑦=−2𝑥+5

6. You Try
2. Ex: 𝑦= 1 2 𝑥+2 𝑦=−𝑥−1

7. Practice
3. Ex: 3𝑥+𝑦=5 𝑥−𝑦=7

8. STEPS Solve each equation for y.
Carefully graph each equation with a STRAIGHT line.
Find the point of intersection (x, y).

9. HOMEWORK
p. 138 #1, 2, graph and find the solution to each system

10. Warm Up (Day 2) Graph each system to find the solution:
𝑥−2𝑦= 𝑦−𝑥= 𝑦=2𝑥−3 6𝑥−3𝑦=9

11. Three Possibilities…

12. How Can You Tell Without Graphing?
Solve each equation for y.
Compare the slopes. If they are DIFFERENT…
the lines will intersect
ONE SOLUTION

13. If BOTH slope and intercepts are the same…
If the slopes are the same, compare the y-intercepts. If those are DIFFERENT…
the lines are parallel
NO SOLUTION
If BOTH slope and intercepts are the same…
the lines coincide
INFINITELY MANY SOLUTIONS.

14. Practice
Without graphing, determine whether the system has one solution, no solutions, or infinitely many solutions.
1. −3𝑥+𝑦=4 𝑥− 1 3 𝑦=1

15. Practice
Without graphing, determine whether the system has one solution, no solutions, or infinitely many solutions.
𝑥+3𝑦=1 4𝑥+𝑦=−3

16. Practice
Without graphing, determine whether the system has one solution, no solutions, or infinitely many solutions.
3. 𝑦=2𝑥−3 6𝑥−3𝑦=9

17. In the Graphing Calculator
Put the two equations into Y1 and Y2.
They MUST be solved for y!
[2nd][CALC][5] for intersect. Hit [ENTER] 3 times, and it will calculate the point (x, y) where they intersect!

18. HOMEWORK (day 2)
p. 139 #17-23 (w/o graphing, determine whether the system has 0, 1, or infinitely many solutions)
#30, 33 (find the solution to the system using the graphing calculator)