Narrated PowerPoint Presentation explaining solving two-variable linear systems of equations using graphs and tables.

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Linear Systems of Equations:

Linear Systems of Equations Solving with two variables 10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 1

Using Graphs and Tables to Solve Linear Systems:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 2 Using Graphs and Tables to Solve Linear Systems S E C T I O N 3 . 1

Definitions:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 3 Systems of Linear Equations Requires 2 variables in two linear equations Solutions are ordered pairs ( x , y ) that makes both equations true Definitions

Example 1:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 4 Example 1 Is (1, 3) a solution to the system? Just plug the coordinates into the system. YES

Example 2:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 5 Example 2 Is (1, –3) a solution to the system? Just plug the coordinates into the system. NO

Steps when graphing:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 6 Graph both equations (y=mx+b) Determine what the intersecting point is and write as a coordinate point Check your point in both equations Steps when graphing

Example 3:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 7 Example 3 Graph these equations and determine the intersection points for this system 1. 2. Start with equation #1 and solve for y:

Example 3:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 8 Example 3 Graph these equations and determine the intersection points for this system 1. 2. Then take equation #2 and solve for y:

Example 3:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 9 Example 3 Graph these equations (4, 4)

Example 3:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 10 Example 3 Check to see if (4, 4) is the accurate solution to the system…

Using Graphing Calculator:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 11 Using Graphing Calculator Graph these equations and determine the intersection points for this system Must be in Y= Form

Using Graphing Calculator:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 12 Using Graphing Calculator Graph these equations and determine the intersection points for this system 2 nd TRACE 5 ENTER ENTER ENTER

Types of Solutions:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 13 Types of Solutions

Example 4:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 14 Example 4 Graph these equations and classify this system Start out with putting both equations into slope-intercept form y = x – 3 y = x – 3

Example 4:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 15 Example 4 Graph these equations and classify this system The system is consistent and dependent with infinitely many solutions.

Your Turn:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 16 Your Turn Graph these equations and classify this system Start out with putting both equations into slope-intercept form 4 x + y = 1 y + 1 = –4 x y = –4 x + 1 y = –4 x – 1

Your Turn:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 17 Your Turn Graph these equations and classify this system The system is inconsistent and has no solution. 4 x + y = 1 y + 1 = –4 x

Example 5:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 18 Example 5 Ravi is comparing the costs of long-distance calling cards. To use the Sprint card it costs 8 cents to connect and then 0.5 cents per minute. The MCI card costs 5 cents to connect and then 0.8 cents per minute to talk. For what number of minutes would calls made with each card cost the same amount?

Example 5:

10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 19 Example 5 Let x represent the number of minutes and y represent the total cost in dollars. Graph and use Calculate/Intersect or TABLE to find the solution. Hint: Use WINDOW settings of Xmin =0, Xmax =20, Ymin =0, Ymax =20. Sprint: y = 8 + .5x MCI: y = 5 + .8x

Example 5:

Example 5 At 10 minutes, it would cost 13 cents for either Sprint’s or MCI’s card. 10/23/2012 10:12:25 PM 3-1: Solving Linear Equations through Graphing and Tables 20 X Y1 Y2 0 8 5 2 9 6.6 4 10 8.2 6 11 9.8 8 12 11.4 10 13 13

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