Q. 105.0( 2 Votes )

Solve the followi

Answer :

Given: - Two equations x + 2y = 1 and 3x + y = 4


Tip: - Theorem – Cramer’s Rule


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







and let Dj be the determinant obtained from D after replacing the jth column by



Then,


provided that D ≠ 0


Now, here we have


x + 2y = 1


3x + y = 4


So by comparing with theorem, lets find D, D1 and D2



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


and



Solving determinant, expanding along 1st row


D2 = 1(4) – (1)(3)


D2 = 4 – 3


D2 = 1


Thus by Cramer’s Rule, we have





and





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