# My systems of equations' mindmap

Mind Map by DaniWEp, updated more than 1 year ago
 Created by DaniWEp about 4 years ago
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### Description

My mindmap of systems of equations

## Resource summary

My systems of equations' mindmap
1 Substitution method
1.1 1) First of all, you have to isolate an unknown like this:
1.1.1 y=24-4x
1.1.2 2) Then, you substitute the isolated unknown in the other equation:
1.1.2.1 2x-3(24-4x)=-2
1.1.2.2 3) Just solve the equation:
1.1.2.2.1 2x+12x=-2+72
1.1.2.2.1.1 14x=70
1.1.2.2.1.1.1 [x=5]
1.1.2.2.1.1.1.1 [y=24-20=4]
1.1.2.2.1.1.1.1.1 (5,4)
1.2 Example: 2x-3y=-2
1.2.1 4x+y=24
2.1 1) In this case, you've to start multiplying one equation in order to equal an unknown in both systems:
2.1.1 (2x-y=9)4
2.1.1.1 8x-4y=36

Annotations:

• 4y
2.1.1.1.1 3x+4y=-14

Annotations:

• 4y
2.1.2 2) Then, you have to remove the equal unknown in one equation like this:
2.1.2.1 3x+4y=-14
2.1.2.1.1 +
2.1.2.1.1.1 8x-4y=36
2.1.2.1.1.1.1 -----------------
2.1.2.1.1.1.1.1 11x=22
2.1.2.1.1.1.1.1.1 [x=2]
2.1.2.1.1.1.1.2 11x=22
2.1.2.2 3) You have just done it
2.1.2.2.1 [x=2]
2.1.2.2.1.1 4-9=y
2.1.2.2.1.1.1 -5=y
2.1.2.2.2 (2, -5)
2.2 Example: 2x–y=9
2.2.1 3x+4y=–14
3 Equalization Method
3.1 1) The first step is to isolate an unknown in both equations:
3.1.1 x=(-7-3y)/2
3.1.1.1 x=(-4+2y)/3
3.1.2 2) Next, you substitute one "x" by the other equation:
3.1.2.1 (-7-3y)/2=(-4+2y)/3
3.1.2.2 3) Solve it now!
3.1.2.2.1 3(-7-3y)=2(-4+2y)
3.1.2.2.1.1 -21+8=-y
3.1.2.2.1.1.1 [13=y]
3.1.2.2.1.1.1.1 [x=-8+26=18]
3.2 Example: 2x+3y=−7
3.2.1 3x−2y=−4
4 Graphical method
4.1 Example: 2x–3y=–2
4.1.1 4x+y =24
4.2 1) This is the most different method; you would find the solution trying with different combinations:
4.2.1 x
4.2.1.1 -2
4.2.1.1.1 -1
4.2.1.1.1.1 0
4.2.1.1.1.1.1 1
4.2.1.1.1.1.1.1 2
4.2.1.1.1.1.2 y=24
4.2.1.1.1.1.2.1 y=20
4.2.1.1.1.1.2.1.1 y=16
4.2.2 y=24-4x
4.2.2.1 y=32
4.2.2.1.1 y=28
4.2.3 2) You have to do it with both equations:
4.2.3.1 x
4.2.3.1.1 -2
4.2.3.1.1.1 -1
4.2.3.1.1.1.1 0
4.2.3.1.1.1.1.1 1
4.2.3.1.1.1.1.1.1 2
4.2.3.1.1.1.1.1.1.1 y=2
4.2.3.1.1.1.2 y=0
4.2.3.1.1.1.2.1 y=0.6^
4.2.3.1.1.1.2.1.1 y=1.3^
4.2.3.1.1.2 y=0.6^
4.2.3.2 y=(2+2x)/3

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