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

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 = – 2

3x + 4y = 3

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

Solving determinant, expanding along 1^st row

⇒ D = 2(4) – (3)( – 1)

⇒ D = 8 + 3

⇒ D = 11

Again,

Solving determinant, expanding along 1^st row

⇒ D₁ = – 2(4) – (3)( – 1)

⇒ D₁ = – 8 + 3

⇒ D₁ = – 5

and

Solving determinant, expanding along 1^st row

⇒ D₂ = 3(2) – ( – 2)(3)

⇒ D₂ = 6 + 6

⇒ D₂ = 12

Thus by Cramer’s Rule, we have

⇒

⇒

and

⇒

⇒