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Solving Systems by Graphing: Easy Techniques & Essential Concepts

Learn to solve systems of equations through graphing, understanding solutions, finding intersections, exploring different scenarios, and identifying no solution or infinitely many solutions. Practice methods and summarize key steps. Perfect guide for mastering graphing systems. Improve your skills with hands-on examples and visual aids.

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Solving Systems by Graphing: Easy Techniques & Essential Concepts

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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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