1. Dear Santa Presents from YOU!
No homework this week!!! 

2. Warm ups
What is the slope and y intercept?

3. 8.1 Graphing Systems of Equations
Objective: To solve systems of equations by graphing.

4. System of Linear Equations:
System of Linear Equations: Two or more linear equations.
A solution to the system of linear equations is any ordered pair that makes BOTH equations true.

5. Three Types of Solutions:
 Intersection is Solution
One Solution
Infinite Solutions
No Solution
Different slope
Different y-intercept
“Intersect at one point”
Same slope
Different y-intercept
“Run parallel  Never intersect”
Same slope
Same y-intercept
“Same line  Intersect infinitely”

6. Examples: Solve each system by graphing.
1) y = –x y = 2x + 4
y = –x + 1
Slope: -1
Y-int: (0, 1)
y = 2x + 4
Slope: 2
Y-int: (0, 4)
Different slope
Different y-intercept
“Intersect at one point”
The solution of the system is: (-1, 2)
x = –1, y = 2

7. 2) x + y = 1 y = –x + 3 x + y = 1 y = –x + 3 –x –x y = - x + 1
Slope: -1
Y-int: (0, 1)
y = –x + 3
Slope: –1
Y-int: (0, 3)
Same slope
Different y-intercept
“Run parallel  Never intersect”
The solution of the system is: no solution

8. “Same line  Intersect infinitely”
3) x – 2y = x – 4y = 8
x – 2y = 4
–x –x
–2y = –x + 4
– –2 –2
y = ½ x – 2
Slope: ½
Y-int: (0, –2)
2x – 4y = 8
–2x –2x
–4y = –2x + 8
– –4 –4
Y = ½ x – 2
Slope: ½
Y-int: (0, –2)
The solution of the system is: infinite solutions
Same slope
Same y-intercept
“Same line  Intersect infinitely”

9. Try with a Partner: 4) y = 3x – 3 x + y = 1 y = 3x – 3 x + y = 1 –x –x
Slope: 3
Y-int: (0, –3 )
x + y = 1
–x –x
y = –x + 1
Slope: –1
Y-int: (0, 1)
Different slope
Different y-intercept
“Intersect at one point”
The solution of the system is: (1, 0)
x = 1, y = 0

10. Summarize: HOW MANY ANSWERS?
Number of Solutions
Slope
Y-Intercept 1
(Ordered Pair)
Different
Same
(No Solution) ∞
(Infinitely Many)

11. TRY ON OWN
8.1 Handout – Graphing Systems of Linear Equations

12. Speaker and Scribe Review

13. Review

14. Review

15. Write in STANDARD

16. Determine Value of r.

17. Homework
8.1 Graphing Systems of Linear Equations (2 sides)