Algebra/Solutions of systems of linear equations

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Algebra

Solutions of systems of linear equations[edit]

A solution of a system of linear equations is a set of numbers for each variable that makes every equation true.

Number of solutions for a system of linear equations

A system can either have

  1. Zero solutions
  2. One solution
  3. Infinitely many solutions

This can be demonstrated using 2 variable sets of equations.

No solutions

\begin{matrix}3x+2y=6\\3x+2y=12\end{matrix}

One solution

\begin{matrix}x-y=1\\3x+y=9\end{matrix}

Infinite solutions

\begin{matrix}x-y=0\\5x-5y=0\end{matrix}