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

x + 2y = 1

3x + y = 4

Given: - Two equations x + 2y = 1 and 3x + y = 4

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

x + 2y = 1

3x + y = 4

So by comparing with theorem, lets find D, D₁ and D₂

Solving determinant, expanding along 1^st row

⇒ D = 1(1) – (3)(2)

⇒ D = 1 – 6

⇒ D = – 5

Again,

Solving determinant, expanding along 1^st row

⇒ D₁ = 1(1) – (2)(4)

⇒ D₁ = 1 – 8

⇒ D₁ = – 7

and

Solving determinant, expanding along 1^st row

⇒ D₂ = 1(4) – (1)(3)

⇒ D₂ = 4 – 3

⇒ D₂ = 1

Thus by Cramer’s Rule, we have

⇒

⇒

⇒

and

⇒

⇒

⇒