Cramer Rule Example





In this page cramer rule example we are going to see examples of cramer rule using two equations.

Example 1

Solve the  following equation using determinant method

 x + 2y = 3

2x + 4y = 8

Δ =
 
1 2
2 4

    =  4 - 4

 ∆ = 0 

Δx =
 
3 2
8 4

    =  12 - 16

= -4 ≠ 0

Δy =
 
1 3
2 8

    =  8 - 6

 ∆ = 2 ≠ 0

Since ∆ = 0, ∆ ≠ 0 and  ∆ ≠ 0the system is consistent and it has no solution.


Example 2

Solve the  following equation using determinant method

 2x + 4y = 6

 6x + 12y = 24

Δ =
 
2 4
6 12

    =  24 - 24

 ∆ = 0 

Δx =
 
6 4
24 12

    =  72 - 96             cramer rule example  cramer rule example

= -24 ≠ 0

Δy =
 
2 6
6 24

    =  48 - 36

 ∆ = 12 ≠ 0

Since ∆ = 0, ∆ ≠ 0 and  ∆ ≠ 0the system is consistent and it has no solution.


Example 3

Solve the  following equation using determinant method

 x + 2y = 3

 5x + 6y = 4

Δ =
 
1 2
5 6

    =  6 - 10

 ∆ = -4 ≠ 0  

Δx =
 
1 2
4 6

    =  6 - 8

= -2 ≠ 0

Δy =
 
1 1
5 4

     =  4 - 5

 ∆ = -1 ≠ 0

Since ∆ = 0, ∆ ≠ 0 and  ∆ ≠ 0the system is consistent and it has no solution.



Example 4

Solve the  following equation using determinant method

 x - 2y = 3

 5x - 10y = 4

Δ =
 
1 -2
5 -10

    =  -10 - (-10)

    =  -10 +10

    =  0

 ∆ = 0   

Δx =
 
3 -2
4 -10

    = -30- (-8)

    = -30 + 8

    = -22

= -10 ≠ 0

Δy =
 
1 3
5 4

    = 4 - 15

    = -11

 ∆ = -11 ≠ 0

Since ∆ = 0, ∆ ≠ 0 and  ∆ ≠ 0the system is consistent and it has no solution.






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