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

2x – y = 1

7x – 2y = – 7

Given: - Two equations 2x – y = 1 and 7x – 2y = – 7

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 – y = 1

7x – 2y = – 7

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

Solving determinant, expanding along 1^st row

⇒ D = 2( – 2) – (7)( – 1)

⇒ D = – 4 + 7

⇒ D = 3

Again,

Solving determinant, expanding along 1^st row

⇒ D₁ = 1( – 2) – ( – 7)( – 1)

⇒ D₁ = – 2 – 7

⇒ D₁ = – 9

and

Solving determinant, expanding along 1^st row

⇒ D₂ = 2( – 7) – (7)(1)

⇒ D₂ = – 14 – 7

⇒ D₂ = – 21

Thus by Cramer’s Rule, we have

⇒

⇒

⇒ x = – 3

and

⇒

⇒

⇒ y = – 7