Solve Systems By Graphing

Systems of Equations
1.0x

Solve Systems By Graphing

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  1. Objective

    Slide 1 - Objective

    • The student will be able to:
    • solve systems of equations by graphing.
    • SOL: A.4e
    • Designed by Skip Tyler, Varina High School
    • Modified by Mr. Burns
  2. Intersecting Lines

    Slide 2 - Intersecting Lines

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

    Slide 3 - 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.
  4. Coinciding Lines

    Slide 4 - 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.
  5. What is the solution of the system graphed below?

    Slide 5 - What is the solution of the system graphed below?

    • (2, -2)
    • (-2, 2)
    • No solution
    • Infinitely many solutions
  6. 1) Find the solution to the following system:

    Slide 6 - 1) Find the solution to the following system:

    • 2x + y = 4
    • x - y = 2
    • Graph both equations. I will graph using x- 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)
  7. Graph the equations.

    Slide 7 - 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 = 4
    • x – y = 2
  8. Check your answer!

    Slide 8 - 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!
  9. 2) Find the solution to the following system:

    Slide 9 - 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
  10. Graph the equations.

    Slide 11 - 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!
  11. Check your answer!

    Slide 12 - 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…
  12. What is the solution of this system?

    Slide 13 - What is the solution of this system?

    • 3x – y = 8
    • 2y = 6x -16
    • (3, 1)
    • (4, 4)
    • No solution
    • Infinitely many solutions
  13. Slide 14

    • Solving a system of equations by graphing.
    • Let's summarize! There are 3 steps to solving 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 – intercept or x- and y-intercepts. Be sure to use a ruler and graph paper!
    • This is the solution! LABEL the solution!
    • Substitute the x and y values into both equations to verify the point is a solution to both equations.