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.