How do I solve a system of linear equations by graphing?

Algebra
Tutor: None Selected Time limit: 1 Day

Nov 13th, 2014

  • Solve the following system by graphing.

    • 2x – 3y = –2
      4
      x +  y = 24

     I know I need a neat graph, so I'll grab my ruler and get started. First, I'll solve each equation for "y=", so I can graph easily:

      2x – 3y = –2
      2x + 2 = 3y(2/3)x + (2/3) = y

      4x + y = 24
      y = –4x + 24

    The second line will be easy to graph using just the slope and intercept, but I'll need a T-chart for the first line.

      x

      y = (2/3)x + (2/3)

      y = –4x + 24

      –4

      –8/3 + 2/3 = –6/3 = –2

      16 + 24 = 40

      –1

      –2/3 + 2/3 = 0

      4 + 24 = 28

      2

      4/3 + 2/3 = 6/3 = 2

      –8 + 24 = 16

      5

      10/3 + 2/3 = 12/3 = 4

      –20 + 24 = 4

      8

      16/3 + 2/3 = 18/3 = 6

      –32 + 24 = –8

    (Sometimes you'll notice the intersection right on the T-chart. Do you see the point that is in both equations above? Check the gray-shaded row above.)

     
    Now that I have some points, I'll grab my ruler and graph neatly, and look for the intersection:

    Even if I hadn't noticed the intersection point in the T-chart, I can certainly see it from the picture.


     

      solution:  (x, y) = (5, 4)


Nov 13th, 2014

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Nov 13th, 2014
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