Given: - Two equations 2x – y = 17 and 3x + 5y = 6

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 = 17

3x + 5y = 6

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

Solving determinant, expanding along 1^st row

⇒ D = 2(5) – (3)( – 1)

⇒ D = 10 + 3

⇒ D = 13

Again,

Solving determinant, expanding along 1^st row

⇒ D₁ = 17(5) – (6)( – 1)

⇒ D₁ = 85 + 6

⇒ D₁ = 91

and

Solving determinant, expanding along 1^st row

⇒ D₂ = 2(6) – (17)(3)

⇒ D₂ = 12 – 51

⇒ D₂ = – 39

Thus by Cramer’s Rule, we have

⇒

⇒

⇒ x = 7

and

⇒

⇒

⇒ y = – 3