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Graphing Systems of Equations: Bell Ringer Activity

Learn to solve systems of equations by graphing intersecting, parallel, and coinciding lines to find unique, no, or infinite solutions. Practice solving systems with step-by-step instructions.

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Graphing Systems of Equations: Bell Ringer Activity

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  1. Bell Ringer Solve the following equations for y: 1. x + y = -3 2. 3y – 2x = 15 3. 5x – y = 7

  2. Objective The student will be able to: solve systems of equations by graphing. SOL: A.9

  3. 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 ALL of the equations. This point will be an ordered pair. • When graphing, you will encounter three possibilities.

  4. Intersecting Lines • The point where the lines intersect is your solution. • The solution of this graph is (1, 2) (1,2)

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

  6. Coinciding Lines • These lines are the same! • Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS! • Coinciding lines have the same slope and y-intercepts.

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

  8. 1) Find the solution to the following system: 2x + y = 4 x - y = 2 Graph both equations. I will use slope intercept form. y = -2x + 4 slope = -2 Point (0,4) y = x -2 slope = 1 Point (0, -2)

  9. Graph the equations. y = -2x + 4 slope = -2 Point (0,4) y = x -2 slope = 1 Point (0, -2) Where do the lines intersect? (2, 0) 2x + y = 4 x – y = 2

  10. Check your answer! To check your answer, plug the point back into both equations. 2x + y = 4 2(2) + (0) = 4 x - y = 2 (2) – (0) = 2 Nice job…let’s try another!

  11. 2) Find the solution to the following system: y = 2x – 3 -2x + y = 1 Graph both equations. Put both equations in slope-intercept or standard form. I’ll do slope-intercept form on this one! y = 2x – 3 y = 2x + 1 Graph using slope and y-intercept

  12. Graph the equations. 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!

  13. Check your answer! Not a lot to check…Just make sure you set up your equations correctly. I double-checked it and I did it right…

  14. What is the solution of this system? • (3, 1) • (4, 4) • No solution • Infinitely many solutions 3x – y = 8 2y = 6x -16

  15. 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.

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