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)