Mind map
My systems of equations' mindmap
Map content
My systems of equations' mindmap
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)
- [y=24-20=4]
- [x=5]
- 14x=70
- 2x+12x=-2+72
- Example: 2x-3y=-2
- 4x+y=24
- 1) First of all, you have to isolate an unknown like this:
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
- 8x-4y=36
- 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
- 11x=22
- -----------------
- 8x-4y=36
- +
- 3) You have just done it
- [x=2]
- 4-9=y
- -5=y
- 4-9=y
- (2, -5)
- [x=2]
- 3x+4y=-14
- (2x-y=9)4
- Example: 2x–y=9
- 3x+4y=–14
- 1) In this case, you've to start multiplying one equation in order to equal an unknown in both systems:
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]
- [13=y]
- -21+8=-y
- 3(-7-3y)=2(-4+2y)
- x=(-7-3y)/2
- Example: 2x+3y=−7
- 3x−2y=−4
- 1) The first step is to isolate an unknown in both equations:
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=20
- 1
- 0
- -1
- -2
- y=24-4x
- y=32
- y=28
- y=32
- 2) You have to do it with both equations:
- x
- -2
- -1
- 0
- 1
- 2
- y=2
- 2
- 1
- y=0
- y=0.6^
- y=1.3^
- y=0.6^
- 0
- y=0.6^
- -1
- -2
- y=(2+2x)/3
- x
- x
- Example: 2x–3y=–2