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--- lecture_2_sides [2016/01/24 16:31] – rupert
+++ lecture_2_sides [2016/01/24 16:44] (current) – rupert
@@ Line 37: / Line 37: @@
 $ x+3y+z=5$ and $ 2x+7y+4z=17$.
-  * Here's a picture of the two planes:<html><iframe scrolling="no" src="https://tube.geogebra.org/material/iframe/id/529147/width/800/height/503/border/888888/rc/true/ai/false/sdz/true/smb/false/stb/true/stbh/true/ld/false/sri/true/at/auto" width="800px" height="503px" style="border:0px;"> </iframe></html>
+  * <html><iframe scrolling="no" src="https://tube.geogebra.org/material/iframe/id/529147/width/800/height/503/border/888888/rc/true/ai/false/sdz/true/smb/false/stb/true/stbh/true/ld/false/sri/true/at/auto" width="800px" height="503px" style="border:0px;"> </iframe></html>
 ==== Intersection of $ x+3y+z=5$ and $ 2x+7y+4z=17$ ====
   * To find the equation of the line of intersection, we must find the points which are solutions of //both// equations at the same time.
-  * Eliminating variables, we get
+  * Eliminating variables, we get $x=-16+5z$, $y=7-2z$
-\[ x=-16+5z,\quad y=7-2z\]
+  * The line of intersection consists of the points $(-16+5z,7-2z,z)$, where $z\in\mathbb{R}$
-which tells us that for any value of $z$, the point
-\[ (-16+5z,7-2z,z)\]
-is a typical point in the line of intersection.