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

2x + 3y = 10

x + 6y = 4

Given: - Two equations 2x – 3y = 10 and x + 6y = 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

2x + 3y = 10

x + 6y = 4

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

Solving determinant, expanding along 1^st row

⇒ D = 2(6) – (3)(1)

⇒ D = 12 – 3

⇒ D = 9

Again,

Solving determinant, expanding along 1^st row

⇒ D₁ = 10(6) – (3)(4)

⇒ D = 60 – 12

⇒ D = 48

and

Solving determinant, expanding along 1^st row

⇒ D₂ = 2(4) – (10)(1)

⇒ D₂ = 8 – 10

⇒ D₂ = – 2

Thus by Cramer’s Rule, we have

⇒

⇒

⇒

and

⇒

⇒

⇒