SystemsOfEquations

# 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}↔ k_{1}E_{1}+k_{2}E_{2}+…+k_{i}E_{i}+…k_{m}E_{m}, k_{i} ≠ 0, k_{j} are real numbers, j = 1, 2, ….m

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