From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Wed, 30 Jan 2019 09:45:15 +0000 (+1100)
Subject: polynomials - simultaneous equations & linear stuff
X-Git-Tag: yr12~272
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/fea35021ef877b538e1e93090fcb3d73ea5f40f0?ds=inline;hp=f8e66a8cce42723d3e0a03c71872c91a4d819fb4

polynomials - simultaneous equations & linear stuff
---

diff --git a/methods/polynomials.md b/methods/polynomials.md
index b80ea63..02dc629 100644
--- a/methods/polynomials.md
+++ b/methods/polynomials.md
@@ -48,3 +48,16 @@ $$=a(x-b)(x-c)^3$$
 
 where
 - $x$-intercepts at $x=b,c,d,e$
+
+## Literal equations
+
+Equations with multiple pronumerals. Solutions are expressed in terms of pronumerals (parameters))
+
+## Simultaneous equations (linear)
+
+- Unique solution - lines intersect at point
+- Infinitely many solutions - lines are equal
+- No solution - lines are parallel
+
+Solving in matrix form - use inverse $A^{-1}= {1 \over {ad-bc}}\begin{bmatrix}d & -b \\ -c & a\end{bmatrix}$. $A^{-1}$ exists for infinite solutions or no solutions ($ad-bc=0$), does not exist for unique solutions ($ad-bc \ne 0$).  
+Or use `det` on CAS.
\ No newline at end of file