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

x – 2y = 4

– 3x + 5y = – 7

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

Solving determinant, expanding along 1^st row

⇒ D = 5(1) – ( – 3)( – 2)

⇒ D = 5 – 6

⇒ D = – 1

Again,

Solving determinant, expanding along 1^st row

⇒ D₁ = 5(4) – ( – 7)( – 2)

⇒ D₁ = 20 – 14

⇒ D₁ = 6

and

Solving determinant, expanding along 1^st row

⇒ D₂ = 1( – 7) – ( – 3)(4)

⇒ D₂ = – 7 + 12

⇒ D₂ = 5

Thus by Cramer’s Rule, we have

⇒

⇒

⇒ x = – 6

and

⇒

⇒

⇒ y = – 5