Marty Supreme
Answer
The “two‑step” method you used is a standard way to solve a linear system with a single right‑hand side.
The first step is to reduce the coefficient matrix to an upper‑triangular form (Gaussian elimination).
The second step is to solve the triangular system by back‑substitution.
In the literature this is usually called Gaussian elimination (or LU factorisation when the factorisation is stored).
If you want to emphasise that the matrix is first transformed and then the system is solved, you can say “Gaussian elimination followed by back‑substitution.”
So the correct name for the whole procedure is Gaussian elimination (or LU decomposition), and the second part is back‑substitution.
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