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 = 

= 4  4
∆ = 0
Δ_{x} = 

= 12  12
∆ₓ = 0
Δ_{y} = 

= 12  12
∆ᵧ = 0
Since ∆ = 0, ∆ₓ = 0 and ∆ᵧ = 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 = 

= 6  6
∆ = 0
Δ_{x} = 

= 9  9
∆ₓ = 0
Δ_{y} = 

= 18  18
∆ᵧ = 0
Since ∆ = 0, ∆ₓ = 0 and ∆ᵧ
= 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 =(3k)/2
y = k cramer rule examples
Solution:
x = (3  k)/2
y = k here k ∈ R