My systems of equations' mindmap

Substitution method
1. 1) First of all, you have to isolate an unknown like this:
  1. y=24-4x
  2. 2) Then, you substitute the isolated unknown in the other equation:
    1. 2x-3(24-4x)=-2
    2. 3) Just solve the equation:
      1. 2x+12x=-2+72
        14x=70
        [x=5]
        [y=24-20=4]
        (5,4)
2. Example: 2x-3y=-2
  1. 4x+y=24
Addition/Substraction method
1. 1) In this case, you've to start multiplying one equation in order to equal an unknown in both systems:
  1. (2x-y=9)4
    1. 8x-4y=36
      Annotations:
      - 4y
      1. 3x+4y=-14
        Annotations:
        4y
  2. 2) Then, you have to remove the equal unknown in one equation like this:
    1. 3x+4y=-14
      1. +
        8x-4y=36
        -----------------
        11x=22
        [x=2]
        11x=22
    2. 3) You have just done it
      1. [x=2]
        4-9=y
        -5=y
      2. (2, -5)
2. Example: 2x–y=9
  1. 3x+4y=–14
Equalization Method
1. 1) The first step is to isolate an unknown in both equations:
  1. x=(-7-3y)/2
    1. x=(-4+2y)/3
  2. 2) Next, you substitute one "x" by the other equation:
    1. (-7-3y)/2=(-4+2y)/3
    2. 3) Solve it now!
      1. 3(-7-3y)=2(-4+2y)
        -21+8=-y
        [13=y]
        [x=-8+26=18]
2. Example: 2x+3y=−7
  1. 3x−2y=−4
Graphical method
1. Example: 2x–3y=–2
  1. 4x+y =24
2. 1) This is the most different method; you would find the solution trying with different combinations:
  1. x
    1. -2
      1. -1
        0
        1
        2
        y=24
        y=20
        y=16
  2. y=24-4x
    1. y=32
      1. y=28
  3. 2) You have to do it with both equations:
    1. x
      1. -2
        -1
        0
        1
        2
        y=2
        y=0
        y=0.6^
        y=1.3^
        y=0.6^
    2. y=(2+2x)/3

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My systems of equations' mindmap

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	Created by Dani Calvo about 8 years ago