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Solve systemsbygraphing

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Solve systemsbygraphing

  1. 1. ObjectiveThe student will be able to:solve systems of equations by graphing.
  2. 2. What is a system of equations?A system of equations is when you havetwo or more equations using the samevariables.The solution to the system is the pointthat satisfies ALL of the equations. Thispoint will be an ordered pair.When graphing, you will encounter threepossibilities.
  3. 3. Intersecting LinesThe point where the linesintersect is your solution.The solution of this graphis (1, 2)(1,2)
  4. 4. Parallel Lines These lines neverintersect! Since the lines nevercross, there isNO SOLUTION! Parallel lines have thesame slope with differenty-intercepts.2Slope = = 21y-intercept = 2y-intercept = -1
  5. 5. Coinciding Lines These lines are the same! Since the lines are on topof each other, there areINFINITELY MANYSOLUTIONS! Coinciding lines have thesame slope andy-intercepts.2Slope = = 21y-intercept = -1
  6. 6. What is the solution of the systemgraphed below?1. (2, -2)2. (-2, 2)3. No solution4. Infinitely many solutions
  7. 7. 1) Find the solution to the followingsystem:2x + y = 4x - y = 2Graph both equations. I will graph usingx- and y-intercepts (plug in zeros).Graph the ordered pairs.2x + y = 4(0, 4) and (2, 0)x – y = 2(0, -2) and (2, 0)
  8. 8. Graph the equations.2x + y = 4(0, 4) and (2, 0)x - y = 2(0, -2) and (2, 0)Where do the lines intersect?(2, 0)2x+y=4x – y =2
  9. 9. Check your answer!To check your answer, plugthe point back into bothequations.2x + y = 42(2) + (0) = 4x - y = 2(2) – (0) = 2 Nice job…let’s try another!
  10. 10. 2) Find the solution to the followingsystem:y = 2x – 3-2x + y = 1Graph both equations. Put both equationsin slope-intercept or standard form. I’ll doslope-intercept form on this one!y = 2x – 3y = 2x + 1Graph using slope and y-intercept
  11. 11. Graph the equations.y = 2x – 3m = 2 and b = -3y = 2x + 1m = 2 and b = 1Where do the lines intersect?No solution!Notice that the slopes are the same with differenty-intercepts. If you recognize this early, you don’thave to graph them!
  12. 12. Check your answer!Not a lot to check…Justmake sure you set upyour equations correctly.I double-checked it and Idid it right…
  13. 13. What is the solution of this system?3x – y = 82y = 6x -161. (3, 1)2. (4, 4)3. No solution4. Infinitely many solutions
  14. 14. Solving a system of equations by graphing.Lets summarize! There are 3 steps tosolving a system using a graph.Step 1: Graph both equations.Step 2: Do the graphs intersect?Step 3: Check your solution.Graph using slope and y – interceptor x- and y-intercepts. Be sure to usea ruler and graph paper!This is the solution! LABEL thesolution!Substitute the x and y values intoboth equations to verify the point isa solution to both equations.

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