A system of [[Linear]] equations are a series of equations relating two or more [[Variable|Variables]] to each other, with the restriction that only [[Linear Transformation|Linear Transformations]] are applied to said variables (*for example*, you won't ever see something like $x_1^2$ or $\sqrt{{y} }$). ### Representing as Row Echelon Form [[Row Echelon Form]] is a way of representing a linear equation in order to treat it as a kind of [[Matrix|Matrix]], making it generally easier / more reliable to work with. >[!example] >$\cases{ >x+y-3z=-2 \\ >-x+y-z=0\\ >2x+y+2z=9 >}$ Because we always right system of equations with the same notation, *eg.* $ax+by+cz=d$, etc, we can write the notation as an [[../../02 Areas/Math/Augmented Matrix|Augmented Matrix]]: >[!example] >$\rowechelon{ >1&1&-3&-2\\ >-1&1&-1&0\\ >2&1&2&9 >}$