Grade Distribution 2nd 5th A 5 B 4 8 C 2 D F 13 7 3 100+ 1 Avg 71.96 No Shows 3 100+ 1 Avg 71.96 76.35 1

Using Graphs and Tables to Solve Linear Systems S E C T I O N 3 . 1 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Definitions Systems of Linear Equations Requires 2 variables into two linear standard form equations Solutions are systems of ordered pairs (x, y) 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Example 1 Is (1, 3) a solution to the system, Plug the coordinates into the system,. YES 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Your Turn Is (–1, 6) a solution to the system, Plug the coordinates into the system,. NO 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Steps when graphing Graph both equations (preferably on y-intersect form) Determine what the intersecting point is and put it in coordinate form Check your point to both equations 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Example 2 Graph these equations and determine the intersection points for this system, Start out with the first equation and put it in y= form 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Example 2 Graph these equations and determine the intersection points for this system, Find out the second equation and put it in y= form 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Example 2 Graph these equations (4, 4) 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Example 2 Check to see if (4, 4) is the accurate solution to the system,… 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Example 3 Graph these equations and determine the intersection points for this system, Start out with the first equation and put it in y= form 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Example 3 Graph these equations and determine the intersection points for this system, Find out the second equation and put it in y= form 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Example 3 Graph these equations (1, 3) 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Example 3 Check to see if (1, 3) is the accurate solution to the system,… 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Your Turn Graph these equations and determine the intersection points for this system, (3, –1) 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

Using Graphing Calculator Graph these equations and determine the intersection points for this system, Must be in Y= Form 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

Using Graphing Calculator Graph these equations and determine the intersection points for this system, 2nd TRACE 5 ENTER 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Types of Solutions Put the equations into slope-intercept form Determine the equation by looking the slope of the system Determine the solution Consistent Solution: A system, that has at least ONE solution Inconsistent Solution: A system, that has NO solution Independent Solution: A system, that has EXACTLY one solution Dependent Solution: A system, that has INFINITE amount of solutions 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Types of Solutions 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

Flowchart INCONSISTENT CONSISTENT INDEPENDENT DEPENDENT How many solutions does it have? INCONSISTENT (No Solution) CONSISTENT (At least 1 Solution) How many points do they intersect? All points (overlap) 1 point INDEPENDENT DEPENDENT 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Example 4 Graph these equations and determine the intersection points for this system, Start out with putting both equations into slope-intercept form 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Example 4 Graph these equations and determine the intersection points for this system, The system, is consistent and dependent with infinitely many solutions. 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Your Turn Graph these equations and determine the intersection points for this system, The system, is inconsistent and has no solution. 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Example 5 City Park Golf Course charges $20 to rent golf clubs plus $55 per hour for golf cart rental. Sea Vista Golf Course charges $35 to rent clubs plus $45 per hour to rent a cart. For what number of hours is the cost of renting clubs and a cart the same for each course? 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Example 5 Let x represent the number of hours and y represent the total cost in dollars. City Park Golf Course: y = 55x + 20 Sea Vista Golf Course: y = 45x + 35 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Example 5 Use increments of ½ to represent 30 min. y = 55x + 20 y = 45x + 35 When x = 1 1/2, the y-values are both 102.5. The cost of renting clubs and renting a cart for 1 1/2 hours is $102.50 at either company. So the cost is the same at each golf course for 1 1/2 hours. x y 20 ½ 47.5 1 75 1 1/2 102.5 2 120 x y 35 ½ 57.5 1 80 1 1/2 102.5 2 125 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables

3-1: Solving Linear Equations through Graphing and Tables Assignment Pg 156 15-29 odd, 35 11/29/2018 2:06 AM 3-1: Solving Linear Equations through Graphing and Tables