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(Σ)     −3x − 6y + 7z = 4 On commence par faire apparaître en première position (première équation) une équation dans laquelle la variable x est affectée d’un coefficient non nul (1) , et cela au moyen d’un échange d’équations (opération élémentaire) ; faisons le choix d’échanger E1 et E2 , ce que nous noterons E1 ↔ E2 :   x + 4y + 2z = −1 2y − z = 3        x + 4y + 2z = −1  2y − z = 3 (Σ)  − − − (Σ1 )  − −→     E1 ↔E2   −3x − 6y + 7z = 4 −3x − 6y + 7z = 4 Les étapes suivantes

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