Solve the linear system by Gaussian elimination {−2b+3c=1, 3a+6b−3c=−2, 6a+6b+3c=5 An inconsistent linear system with the third row being 0 0 0 6.?

Solve the linear system by Gaussian elimination
$\left\{\begin{array}{l}-2b+3c=1\\ 3a+6b-3c=-2\\ 6a+6b+3c=5\end{array}$
An inconsistent linear system with the third row being 0 0 0 6?
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Jaelyn Levine
Your calculations are correct, since you end up with the last line of the matrix being 0 0 0 6 the last equation in the reduced matrix has no solution so the whole system has no solution