Cramer Rule Examples





In this page cramer rule examples 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 = 6

Δ =
 
1 2
2 4

    =  4 - 4

 ∆ = 0 

Δx =
 
3 2
6 4

    =  12 - 12

 ∆ = 0 

Δy =
 
1 3
2 6

    =  12 - 12

 ∆ = 0 

Since ∆ = 0, ∆ = 0 and  ∆ = 0 and atleast one of the element in ∆ is non zero. Then the system is consistent and it has infinitely many solution. The above system is reduced into single equation. To solve this equation we have to assign y = k.

 x + 2y = 3

 x + 2 (k) = 3

 x + 2k = 3

       x = 3 - 2k

       y = k        

Solution:

 x = 3 - 2k

 y = k     here k ∈ R


Example 2

Solve the  following equation using determinant method

2x + y = 3

6x + 3y = 9

Δ =
 
2 1
6 3

    =  6 - 6

 ∆ = 0 

Δx =
 
3 1
9 3

    =  9 - 9

 ∆ = 0 

Δy =
 
2 3
6 9

    =  18 - 18

 ∆ = 0 

Since ∆ = 0, ∆ = 0 and  ∆ = 0 and atleast one of the element in ∆ is non zero. Then the system is consistent and it has infinitely many solution. The above system is reduced into single equation. To solve this equation we have to assign y = k.

2x + y = 3

2x + k = 3

2x + k = 3

       2x = 3 - k

        x =(3-k)/2

        y = k         cramer rule examples

Solution:

 x = (3 - k)/2

 y = k     here k ∈ R






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