## 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  