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Home > Algebra calculators > Cramer's Rule method example
7. Cramer's Rule Method example ( Enter your problem )
( Enter your problem )
  1. Examples
 		Other related methods
  1. Substitution method
  2. Elimination method
  3. Cross Multiplication method
  4. Addition-Substraction method
  5. Graphical method
  6. Inverse matrix method
  7. Cramer's Rule method
6. Inverse matrix method
(Previous method)

1. Examples


1. Solve linear equations x+y=2 and 2x+3y=4 using Cramer's Rule Method

Solution:
The equations can be expressed as
`x+y-2=0`

`2x+3y-4=0`

Use Cramer's Rule to find the values of x, y, z.
`(x)/D_x=(-y)/D_y=(1)/D`

`D_x` = 
 `1`  `-2` 
 `3`  `-4` 


`=1 × (-4) - (-2) × 3`

`=-4 +6`

`=2`


`D_y` = 
 `1`  `-2` 
 `2`  `-4` 


`=1 × (-4) - (-2) × 2`

`=-4 +4`

`=0`


`D` = 
 `1`  `1` 
 `2`  `3` 


`=1 × 3 - 1 × 2`

`=3 -2`

`=1`


`(x)/D_x=(-y)/D_y=(1)/D`

`:.(x)/2=(-y)/0=(1)/1`

`:.(x)/2=(1)/1,(-y)/0=(1)/1`

`:.x=(2)/(1),y=(0)/(1)`

`:.x=2,y=0`

2. Solve linear equations 2x+7y-11=0 and 3x-y-5=0 using Cramer's Rule Method

Solution:
The equations can be expressed as
`2x+7y-11=0`

`3x-y-5=0`

Use Cramer's Rule to find the values of x, y, z.
`(x)/D_x=(-y)/D_y=(1)/D`

`D_x` = 
 `7`  `-11` 
 `-1`  `-5` 


`=7 × (-5) - (-11) × (-1)`

`=-35 -11`

`=-46`


`D_y` = 
 `2`  `-11` 
 `3`  `-5` 


`=2 × (-5) - (-11) × 3`

`=-10 +33`

`=23`


`D` = 
 `2`  `7` 
 `3`  `-1` 


`=2 × (-1) - 7 × 3`

`=-2 -21`

`=-23`


`(x)/D_x=(-y)/D_y=(1)/D`

`:.(x)/-46=(-y)/23=(1)/-23`

`:.(x)/-46=(1)/-23,(-y)/23=(1)/-23`

`:.x=(-46)/(-23),y=(-23)/(-23)`

`:.x=2,y=1`

3. Solve linear equations 3x-y=3 and 7x+2y=20 using Cramer's Rule Method

Solution:
The equations can be expressed as
`3x-y-3=0`

`7x+2y-20=0`

Use Cramer's Rule to find the values of x, y, z.
`(x)/D_x=(-y)/D_y=(1)/D`

`D_x` = 
 `-1`  `-3` 
 `2`  `-20` 


`=-1 × (-20) - (-3) × 2`

`=20 +6`

`=26`


`D_y` = 
 `3`  `-3` 
 `7`  `-20` 


`=3 × (-20) - (-3) × 7`

`=-60 +21`

`=-39`


`D` = 
 `3`  `-1` 
 `7`  `2` 


`=3 × 2 - (-1) × 7`

`=6 +7`

`=13`


`(x)/D_x=(-y)/D_y=(1)/D`

`:.(x)/26=(-y)/-39=(1)/13`

`:.(x)/26=(1)/13,(-y)/-39=(1)/13`

`:.x=(26)/(13),y=(39)/(13)`

`:.x=2,y=3`

4. Solve linear equations 2x-y=11 and 5x+4y=1 using Cramer's Rule Method

Solution:
The equations can be expressed as
`2x-y-11=0`

`5x+4y-1=0`

Use Cramer's Rule to find the values of x, y, z.
`(x)/D_x=(-y)/D_y=(1)/D`

`D_x` = 
 `-1`  `-11` 
 `4`  `-1` 


`=-1 × (-1) - (-11) × 4`

`=1 +44`

`=45`


`D_y` = 
 `2`  `-11` 
 `5`  `-1` 


`=2 × (-1) - (-11) × 5`

`=-2 +55`

`=53`


`D` = 
 `2`  `-1` 
 `5`  `4` 


`=2 × 4 - (-1) × 5`

`=8 +5`

`=13`


`(x)/D_x=(-y)/D_y=(1)/D`

`:.(x)/45=(-y)/53=(1)/13`

`:.(x)/45=(1)/13,(-y)/53=(1)/13`

`:.x=(45)/(13),y=(-53)/(13)`

`:.x=45/13,y=-53/13`



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6. Inverse matrix method
(Previous method)


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