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Question -

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

x + 2y = 1

3x + y = 4



Answer -

Let there be a systemof n simultaneous linear equations and with n unknown given by

Solving determinant,expanding along 1st row

⇒ D = 1(1) – (3)(2)

⇒ D = 1 – 6

⇒ D = – 5

Again,

Solving determinant,expanding along 1st row

⇒ D1 =1(1) – (2) (4)

⇒ D1 =1 – 8

⇒ D1 =– 7

Solving determinant,expanding along 1st row

⇒ D2 =1(4) – (1) (3)

⇒ D2 =4 – 3

⇒ D2 =1

Thus by Cramer’s Rule,we have

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