1. Lesson 3.1 Solving Linear Systems by Graphing
A system of two linear equation in two variables, x and y, consists of two equations of the form: 𝐴𝑥+𝐵𝑦=𝐶 𝐷𝑥+𝐸𝑦=𝐹
A solution to a system of linear equations is an ordered pair (x, y) that satisfies both equations…the point where they intersect!

2. Concept #1 Is a point a solution to a system?
Plug point into both equations. If they are both true , then the point is the solution.

3. Check each point to determine if it is a solution to the following system: 𝑥−3𝑦=−5 −2𝑥+3𝑦=10
Example 1. (1, 4)
Example (-5, 0)

4. Solve each system by graphing. Use quick Graphs.
𝑥−2𝑦=−8 2𝑥+2𝑦=4

5. Solve each system by graphing. Use quick Graphs.
𝑥−2𝑦=−8 2𝑥+2𝑦=4

6. 𝑥−3𝑦=−15 2𝑥−𝑦=−8

7. 𝑥−3𝑦=−15 2𝑥−𝑦=−8

8. Concept #2 Number of Solutions of a Linear System:
One Solution: 2 lines intersect at 1 point
Infinite Solutions: 2 lines overlap & share
all points
No Solutions: 2 lines are parallel &
don’t intersect

9. Please Read Directions p.142
HOMEWORK
Please Read Directions p.142
#12-18 (E), 22, 25, 26, 29, 41, 43, 44, 48

10. Lesson 3.1B: Solve the system by graphing with your calculator.
5. 𝑥+2𝑦=−1 4𝑥−3𝑦=−15

11. 6. −𝑥+3𝑦=1 2𝑥+3𝑦=4

12. Do not have to graph.But show slope-int form. Love Bonin
HOMEWORK
Do not have to graph.But show slope-int form. Love Bonin
Find all solutions p.142
#20, 21, 23, 24, 27, 30, 31,
42, 45, 47, 49