View source for Algebra/Solutions of systems of linear equations

===Solutions of systems of linear equations===

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

<table WIDTH="75%"><tr><td style="background-color: #F3F3FF; border: solid 1px #D6D6FF; padding: 1em;" valign=top>

<H2>Number of solutions for a system of linear equations</H2>
A system can either have<br>
1. Zero solutions<br>
2. One solution<br>
3. Infinitely many solutions
</td></tr></table>

This can be demonstrated using 2 variable sets of equations.

No solutions
<math>\begin{matrix}3x+2y=12\\3x+2y=12\end{matrix}</math>
<br>[[Image:Parallel Lines.svg|300px]]<br>

One solution
<math>\begin{matrix}x-y=1\\3x+y=9\end{matrix}</math>
<br>[[Image:Intersecting Lines.svg|300px]]<br>

Infinite solutions
<math>\begin{matrix}x-y=0\\5x-5y=0\end{matrix}</math>
<br>[[Image:Linear function.svg|300px]]<br>

[[Category:Algebra textbook pages]]