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Warm ups
What is the slope and y intercept?
13
2y x 2 3 6x y 1 2( 5)y x
8.1 Graphing Systems of Equations
Objective: To solve systems of equations by graphing.
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.
Three Types of Solutions: Intersection is Solution
One Solution No Solution
Infinite SolutionsSame slope
Different y-intercept“Run parallel Never
intersect”
Same slope Same y-intercept
“Same line Intersect infinitely”
Different slopeDifferent y-
intercept“Intersect at one
point”
Examples: Solve each system by graphing.1) y = –x + 1 y = 2x + 4
y = –x + 1
Slope: -1
Y-int: (0, 1)
y = 2x + 4
Slope: 2
Y-int: (0, 4)
The solution of the system is: (-1, 2)
x = –1, y = 2
Different slopeDifferent y-
intercept“Intersect at one
point”
2) x + y = 1 y = –x + 3
x + y = 1–x –xy = - x + 1
Slope: -1
Y-int: (0, 1)
y = –x + 3
Slope: –1
Y-int: (0, 3)
The solution of the system is: no solution
Same slopeDifferent y-intercept
“Run parallel Never intersect”
3) x – 2y = 4 2x – 4y = 8
x – 2y = 4–x –x–2y = –x + 4–2 –2 –2 y = ½ x – 2
Slope: ½
Y-int: (0, –2)
2x – 4y = 8–2x –2x–4y = –2x + 8–4 –4 –4Y = ½ x – 2
Slope: ½
Y-int: (0, –2)
The solution of the system is: infinite solutionsSame slope Same y-intercept
“Same line Intersect infinitely”
Try with a Partner:4) y = 3x – 3 x + y = 1
y = 3x – 3
Slope: 3
Y-int: (0, –3 )
x + y = 1–x –x y = –x + 1
Slope: –1
Y-int: (0, 1)
The solution of the system is: (1, 0)
Different slopeDifferent y-
intercept“Intersect at one
point”x = 1, y = 0
Summarize:HOW MANY ANSWERS?
Number of Solutions
Slope Y-Intercept
1 (Ordered Pair)
Different SameDifferent
0 (No Solution)
Same Different
∞(Infinitely Many)
Same Same
TRY ON OWN
Answer the four multiple choice questions on the elmo.
Speaker and Scribe Review
1 1
2 5x 3
10x
3 2 4x x 3x
333
8x 88x
Review
5 1 1
8 2
x 3
5x
20x 22 48
5x
5
8 6
x x 20x
Review
5 105
6
x 4x
6x 10 3 6 8x x
6 2 5( 3)x x x NOsolution
Write in STANDARD
( 1, 2)(1,8) 5 3x y
1( 4,6)
2m
2 8x y
Determine Value of r.
5(4, )( , 2)
3r r m
7r
3(3, )( ,5)
5r r m
8r
Homework
8.1 Graphing Systems of Linear Equations
(2 sides)