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Question

# The system of equation x+y+z=2,3xâˆ’y+2z=6 and 3x+y+z=âˆ’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 solutionGiven, the system of equations,x+y+z=23x−y+2z=63x+y+z=−18arranging the above equations in matrix form and calculating the determinant, we get,|A|=∣∣ ∣∣1113−12311∣∣ ∣∣=1(−1−2)−1(3−6)+1(3+3)=−3+3+6=6≠0|A| = determinant of coefficient matrix ≠0Therefore there exists a unique solution

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