Equivalent systems

Two equations are equivalent if they have the same solutions. Example:

Two systems are equivalent if they have the same solutions.

To obtain equivalent systems, we can do the following elementary operations:

–To exchange two equations: E_i ↔ E_j

–To substitute an equation by a linear combination of all the equations: E_i↔ k₁E₁+k₂E₂+…+k_iE_i+…k_mE_m, k_i ≠ 0, k_j are real numbers, j = 1, 2, ….m