My systems of equations' mindmap

My systems of equations' mindmap

1. Substitution method

   • 1) First of all, you have to isolate an unknown like this:
     • y=24-4x
     • 2) Then, you substitute the isolated unknown in the other equation:
       • 2x-3(24-4x)=-2
       • 3) Just solve the equation:
         • 2x+12x=-2+72
           • 14x=70
             • [x=5]
               • [y=24-20=4]
                 • (5,4)
   • Example: 2x-3y=-2
     • 4x+y=24

2. Addition/Substraction method

   • 1) In this case, you've to start multiplying one equation in order to equal an unknown in both systems:
     • (2x-y=9)4
       • 8x-4y=36
         • 4y
         • 3x+4y=-14
           • 4y
     • 2) Then, you have to remove the equal unknown in one equation like this:
       • 3x+4y=-14
         • +
           • 8x-4y=36
             • -----------------
               • 11x=22
                 • [x=2]
               • 11x=22
       • 3) You have just done it
         • [x=2]
           • 4-9=y
             • -5=y
         • (2, -5)
   • Example: 2x–y=9
     • 3x+4y=–14

3. Equalization Method

   • 1) The first step is to isolate an unknown in both equations:
     • x=(-7-3y)/2
       • x=(-4+2y)/3
     • 2) Next, you substitute one "x" by the other equation:
       • (-7-3y)/2=(-4+2y)/3
       • 3) Solve it now!
         • 3(-7-3y)=2(-4+2y)
           • -21+8=-y
             • [13=y]
               • [x=-8+26=18]
   • Example: 2x+3y=−7
     • 3x−2y=−4

4. Graphical method

   • Example: 2x–3y=–2
     • 4x+y =24
   • 1) This is the most different method; you would find the solution trying with different combinations:
     • x
       • -2
         • -1
           • 0
             • 1
               • 2
             • y=24
               • y=20
                 • y=16
     • y=24-4x
       • y=32
         • y=28
     • 2) You have to do it with both equations:
       • x
         • -2
           • -1
             • 0
               • 1
                 • 2
                   • y=2
             • y=0
               • y=0.6^
                 • y=1.3^
           • y=0.6^
       • y=(2+2x)/3