The system of equation `x+y+z=2,3x-y+2z=6a n d3x+y+z=-18` has a unique solution (b) no solution an infinite number of solutions zero solution as the only solution

Explanation

To determine the nature of the solution for the system of equations given by:

1. \( x + y + z = 2 \)
2. \( 3x - y + 2z = 6 \)
3. \( 3x + y + z = -18 \)

we will use Cramer's Rule. This method involves calculating the determinants of matrices formed by the coefficients of the variables and the constants on the right-hand side.

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