Solve the following systems of linear equations by Cramer’s rule:

5x + 7y = – 2

4x + 6y = – 3

Given: - Two equations 5x + 7y = – 2 and 4x + 6y = – 3

Tip: - Theorem – Cramer’s Rule

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

and let D_j be the determinant obtained from D after replacing the j^th column by

Then,

provided that D ≠ 0

Now, here we have

5x + 7y = – 2

4x + 6y = – 3

So by comparing with the theorem, let's find D, D₁ and D₂

Solving determinant, expanding along 1^st row

⇒ D = 5(6) – (7)(4)

⇒ D = 30 – 28

⇒ D = 2

Again,

Solving determinant, expanding along 1^st row

⇒ D₁ = – 2(6) – (7)( – 3)

⇒ D₁ = – 12 + 21

⇒ D₁ = 9

and

Solving determinant, expanding along 1^st row

⇒ D₂ = – 3(5) – ( – 2)(4)

⇒ D₂ = – 15 + 8

⇒ D₂ = – 7

Thus by Cramer’s Rule, we have

⇒

⇒

⇒

and

⇒

⇒

⇒