Question

Solve the system of linear equations by Cramer’s rule 

5x + 7y = -2

4x + 6y = -3

Answer 1

Given 5x + 7y = - 2

4x + 6y = - 3

Suppose there be a system of n simultaneous linear equations with n unknown given by

Suppose D_j be determinant observe from D after replacing the j^th column 

So,

Provide that D ≠ 0

Here

5x + 7y = – 2

4x + 6y = – 3

On comparing with theorem, let's find D,D₁, and D₂

On solving determinant, expanding along 1^st row

⇒ D = 5(6) – (7) (4)

⇒ D = 30 – 28

⇒ D = 2

Again,

On solving determinant, expanding along 1^st row

⇒ D₁ = – 2(6) – (7) (– 3)

⇒ D₁ = – 12 + 21

⇒ D₁ = 9

On solving determinant, expanding along 1^st row

⇒ D₂ = – 3(5) – (– 2) (4)

⇒ D₂ = – 15 + 8

⇒ D₂ = – 7

So by Cramer’s Rule,