Apply Cramer's rule to solve the following simultaneous equations.
(i) 2 x + y + 6 z = 46
5 x − 6 y + 4 z = 15
7 x + 4 y − 3 z = 19
(ii) x + 2y + 3z = 2
x – y + z = 3
5x – 11y + z = 17
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) x = 3, y = 4, z = 6
(ii) x= 
, y = 
, z = k, where k ∈ R
Sol. (i)2x + y + 6z = 46
5x – 6y + 4z = 15
7x + 4y – 3z = 19
Δ = 
= 419, Δ x = 
= 1257,
Δ y = 
= 1676, Δ z = 
= 2514
x = 
= 3, y = 
= 4, z = 
= 6
(ii) x + 2y + 3z = 2
x – y + z = 3
5x – 11y + z = 17
Δ = 
= 0, Δ x = 
= 0, Δ y = 
= 0, Δ z = 
= 0
∴ given system of equations has infinite solutions.
Let z = k
x + 2y = 2 – 3k
x – y = 3 – k
∴ x= 
, y = 
, z = k, where k ∈ R
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