01 Graphing Systems.notebook

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April 28, 2014

Steps for Graphing a Line

Steps for Graphing a Line1. Solve for "y"

2. Determine the slope, "m" (convert to fraction if necessary)     and y-intercept, "b"

3. Plot the y-intercept (b)

4. Go up (down) and over (right or left) slope.

5. Connect the dots with a straight edge.

y = mx + b

Graphing Systems of Linear Equations

m =  b = 1

Graphy ­ 2x = 1

y = 3x + 1

+ 2x + 2x y = 2x + 1

m =  b = 

2 = 2/11

3 = 3/1

What point do the lines have in common?

(0, 1)

01 Graphing Systems.notebook

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April 28, 2014

Systems of Linear Equations

Systems of Linear Equations

A system of linear equations is 2 linear equations graphed on the

same coordinate plane.

The solution(s) to a system of linear equations is/arethe point(s) where the 2 lines intersect

Steps for Graphing Systems

Steps for Graphing A System of Linear Equations

1. Solve for "y", and find the  slope"m" & y-intercept"b"      of the 1st line.

2. Graph the 1st line.

3. Solve for "y", and find the  slope"m" & y-intercept"b"      of the 2nd line.

4. Graph the 2nd line.

5. Find the point(s) where the 2 lines intersect.

01 Graphing Systems.notebook

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April 28, 2014

Example #1

1. y = x – 4 y = ­2x + 5

Line #1:m = 1 (= 1/1)b = ­4

Line #2:m = ­2 (= ­2/1)b = 5

Line 1 

Line 2 

(3, -1)Solution:

Example #2

No Solution (∅) because lines are parallel & will never intersect

2. x + y = 3 x + y = 4

Line #1:y = ­x + 3

m = ­1 (= ­1/1)b = 3

Line #2:y = ­x + 4

m = ­1 (= ­1/1)b = 4

Line 1 

Line 2 

Solution 

01 Graphing Systems.notebook

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April 28, 2014

Example #3

3. 2x + y = 3 4x + 2y = 6

Line #1:y = ­2x + 3

m = ­2 (= ­2/1)b = 3Line 1 

Line #2:y = ­2x + 3

m = ­2 (= ­2/1)b = 3Line 2

All points (∞ Solutions) because lines are the sameSolution 

Number of Solutions

Possible Solutions to a System of Linear Equations

No Solutions (∅) 1 Solution ∞ Solutions

Parallel Lines Same LineIntersectingLines

01 Graphing Systems.notebook

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April 28, 2014

MJ ? 13­1

Today's Math Journal QuestionsDay 1 Question: ______________________

(Date)

Today we talked about systems of linear equations.

1) What is a system of linear equations?

2) What is the solution to a system of linear equations?

3) How many solutions are possible to a system of linear equations?

Homework

Homework:Worksheet 13-1