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Question

The system of equation x+y+z=2,3xy+2z=6 and 3x+y+z=18 has

A
unique solution
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B
no solution
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C
an infinite number of solutions
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D
zero solution as the only solution
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Solution

The correct option is B unique solution
Given, the system of equations,

x+y+z=2

3xy+2z=6

3x+y+z=18

arranging the above equations in matrix form and calculating the determinant, we get,

|A|=∣ ∣111312311∣ ∣

=1(12)1(36)+1(3+3)

=3+3+6

=60

|A| = determinant of coefficient matrix 0

Therefore there exists a unique solution

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