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Bellwork 11/12/18

Bellwork 11/12/18. Pg. 228. Chapter 3 Lesson 7 Solving Systems by graphing. Objective. The student will be able to: solve systems of equations by graphing. What is a system of equations?. A system of equations is when you have two or more equations using the same variables.

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Bellwork 11/12/18

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  1. Bellwork 11/12/18 Pg. 228

  2. Chapter 3 Lesson 7 Solving Systems by graphing

  3. Objective The student will be able to: solve systems of equations by graphing.

  4. What is a system of equations? • A system of equations is when you have two or more equations using the same variables. • The solution to the system is the point that satisfies BOTH equations. This point will be an ordered pair (x,y) telling where the two lines intersect aka cross.

  5. Stop & Think!  • How can you use what you already know about equations in slope-intercept form to find the point these two lines have in common? 

  6. What conjecture can you make about the solution to the system shown?  • The point (x,y) where the lines intersect is your solution aka ANSWER! • The solution of this graph is (1, 2) (1,2)

  7. Make an Inference • What inference can you make about two lines with the same slope?  Ex. ) 

  8. Parallel Lines • These lines never intersect! • Since the lines never cross, there is NO SOLUTION! • Parallel lines have the same slope but different y-intercepts.

  9. Identical Lines touch EVERYWHERE! • These lines are the same! • Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS! • They have the exact same slope and y-intercept.

  10. What is the solution of the system graphed below? • (2, -2) • (-2, 2) • No solution • Infinitely many solutions

  11. 1.) Graph both equations to find the solution (x,y) y = -2x+2 y = 2x-2

  12. 2.) Graph the equations to find the solution. y = -2x+4 y = x - 2

  13. 3.) Find the solution to the following system by graphing: y = 2x – 3 y = 2x+1

  14. Explain why in a system with no solution the lines never touch/cross.

  15. y = 2x – 3 m = 2 and b = -3 y = 2x + 1 m = 2 and b = 1 Where do the lines intersect? No solution! Notice that the slopes are the same with different y-intercepts. If you recognize this early, you don’t have to graph them!

  16. 4.) What is the solution of this system? y = 3x+8 y = 3x+8 • (3, 1) • (4, 4) • No solution • Infinitely many solutions

  17. 5.) evaluate the solution to the following system of equations by graphing. 6x - y= 8 -2x +y = 4

  18. 6.) evaluate the solution to the following system of equations by graphing 3x + y = 6 -2x +2y= 12

  19. Page 237

  20. Solving a system of equations by graphing. Let's summarize! There are 3 steps to solving a system using a graph. Graph using slope and y – intercept or x- and y-intercepts. Be sure to use a ruler and graph paper! Step 1: Graph both equations. This is the solution! LABEL the solution! Step 2: Do the graphs intersect? Substitute the x and y values into both equations to verify the point is a solution to both equations. Step 3: Check your solution.

  21. INDEPENDENT PRACTICE Textbook page 239 (1-6)

  22. Exit Ticket 1.) What is the solution to the system? 2.) Describe the 3 different types of  solutions and what they look like on a graph.

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