1 / 25

Intro to Systems of Equations and Graphing

Intro to Systems of Equations and Graphing. b y Tammy Wallace Varina High School. What is a System of Equation?. two or more equations with the same variable being compared. A SYSTEM OF EQUATIONS is: A SOLUTION to the SYSTEM OF EQUATIONS is: A POINT OF INTERSECTION is: .

bazyli
Download Presentation

Intro to Systems of Equations and Graphing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Intro to Systems of Equations and Graphing by Tammy Wallace Varina High School

  2. What is a System of Equation? two or more equations with the same variable being compared. A SYSTEM OF EQUATIONS is: A SOLUTION to the SYSTEM OF EQUATIONS is: A POINT OF INTERSECTION is: the point that both equations have in common: THE POINT OF INTERSECTION the point where both lines meet

  3. Write the solution of each system of equation as an ordered pair. (4, -3) (8, -3) Both systems have only ONE SOLUTION.

  4. Write the solution of each system of equation as an ordered pair. (2, -2) (2, 1)

  5. Write the solution of each system of equation as an ordered pair. Parallel lines do not intersect. Therefore, there is NO SOLUTION!

  6. Write the solution of each system of equation as an ordered pair. What is different about this graph? There appears to only be one line graphed. We call this coinciding lines. Because there are more than one line on top of each other, what can we conclude about the solution set? There are infinite many solutions

  7. Write the solution of each system of equation as an ordered pair. (-3, 0)

  8. Graphing System of Equations When finding the solution to a system of equation, finding the point of intersection is required. To do this, the equations must be graphed. Therefore, the equation must be put in SLOPE-INTERCEPT FORM.

  9. Find the solution set for  3x – 2y = 8 -3x - 3x -2y = -3x + 8 -2 -2 Already in the correct format! 4 -4

  10. Draw each line on the same grid. -4 4 What type of lines are there? What type of solutions do these lines have? What is/are the solution(s) located? Intersecting lines One solution ( 4, 2 )

  11. Find the solution set for 2x + y = 4 - 2x -2x y = -2x + 4 x - y = 2 -x -x -y = -x + 2 y = x - 2 -1( ) 4 -2

  12. Draw each line on the same grid. 1 4 -2 What type of lines are there? What type of solutions do these lines have? What is/are the solution(s) located? Intersecting lines One solution ( 2, 0)

  13. Find the solution set for  2x – y = -1 -2x - 2x -y = -2x - 1 Already in the correct format! -1( ) 1 -3

  14. Graph each equation in the graphing calculatorand answer the following questions. -3 1 Parallel lines • What type of lines are there? • What type of solutions are there? • What do you notice about the equations when they are in slope intercept form AND do you think this has an effect on the solution? NO SOLUTIONS When the equations are in slope-intercept form, you notice the slopes are the same. When the slopes are the same, the lines will be parallel and have solution.

  15. Find the solution set for 3x - y = 8 - 3x -3x -y = -3x + 8 y = 3x - 8 2y = 6x - 16 2 2 y = 3x - 8 -1( ) -8 -8

  16. Graph each equation in the graphing calculatorand answer the following questions. 8 8 Coinciding lines • What type of lines are there? • What type of solutions are there? • What do you notice about the equations when they are in slope intercept form AND do you think this has an effect on the solution? Infinite many solutions When the equations are in slope-intercept form, you notice the equations are the same. When the equations are the same, there are infinite many solutions.

  17. Application of Systems of Equations

  18. When you are given a word problem, remember to do the following: Rewrite the first equation algebraically using the variables chosen. Rewrite the first equation in slope-intercept form and graph. Determine the what the unknown variables are and what letter they will represent. Rewrite what the first equation could be. Rewrite the second equation algebraically using the variables chosen. Rewrite the second equation in slope-intercept form and graph. Rewrite what the second equation could be. Finally, find the solution set using the calculator.

  19. The school is selling tickets to a band concert. On the first day of ticket sales, the school sold 3 adult tickets and 1 student tickets for a total of $28. The school took in $32 on the second day by selling 3 adult tickets and 2 student tickets. Find the price of a student ticket and an adult ticket. a = cost of adult tickets (let a = x) s = cost of student tickets (let s= y) 3x + y = 28 - 3x -3x y = -3x + 28 The school sold 3 adult tickets and 1 student ticket for $28 3x + y = 28 • 3x + 2y = 32 • 3x -3x • 2y = -3x + 32 • 2 2 The school sold 3 adult tickets and 2 student ticks for $32 3x + 2y = 32

  20. The school is selling tickets to a band concert. On the first day of ticket sales, the school sold 3 adult tickets and 1 student tickets for a total of $28. The school took in $32 on the second day by selling 3 adult tickets and 2 student tickets. Find the price of a student ticket and an adult ticket. Solution set is (8, 4)

  21. The solution is located at (8, 4). Graph each equation. Where is the solution set located? Remember what x and y equals when it relates the word problem: x = ______________ and y = _____________ What does the solution set mean? cost of adult tickets cost of student tickets Adult tickets cost $8 each and student tickets cost $4 each.

  22. You are getting ready to move and have asked some friends to help. For lunch, you buy the following sandwiches at the local deli for $30: six ham sandwiches and six turkey sandwiches. Later at night, everyone is hungry again and you buy four ham sandwiches and eight turkey sandwiches for $30.60. What is the price of each sandwich? h = ham sandwiches (let h = x) t = tuna sandwiches (let t = y) 6x + 6y = 30 - 6x -6x 6y = -6x + 30 6 6 y = -x + 5 6 ham and 6 turkey for $30 6x + 6y = 30 4x + 8y = 30.20 -4x -4x 8y = -4x + 30.20 8 8 4 ham and 8 turkey for $30.60 4x + 8y = 30.20

  23. You are getting ready to move and have asked some friends to help. For lunch, you buy the following sandwiches at the local deli for $30: six ham sandwiches and six turkey sandwiches. Later at night, everyone is hungry again and you buy four ham sandwiches and eight turkey sandwiches for $30.60. What is the price of each sandwich? Solution set is (2, 3)

  24. The solution is located at (2, 3). Graph each equation. Where is the solution set located? Remember what x and y equals when it relates the word problem: x = ______________ and y = _____________ What does the solution set mean? cost of ham sandwiches cost of turkey sandwiches Ham sandwiches cost $2 each and turkey sandwiches cost $3 each.

  25. The concession stand is selling hot dogs and hamburgers during a game. At halftime, they sold a total of 50 hot dogs and hamburgers and brought in $105.50. How many of each item did they sell if hamburgers sold for $1.50 and hot dogs sold for $1.25? x + y = 50 - x -x y = -x + 50 50 hotdog and hamburgers were sold h = hotdogs (let h = x) b = hamburgers (let b= y) x + y = 50 0.5x + y = 75.5 -0.5x -0.5x y = -0.5x + 75.5 With selling hotdogs for .50 and hamburgers for $1, $105.50 was made. 0.5x + y = 75.50

More Related