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--- lecture_1_slides_test [2016/01/23 09:40] – rupert
+++ lecture_1_slides_test [2016/01/24 16:22] (current) – rupert
@@ Line 6: / Line 6: @@
 ==== First example: a linear equation in two variables ====
-Consider the equation \[ 2x+5y=7.\]
+  * Consider the equation \[ 2x+5y=7.\]
-This is an equation in two //[[variables]]//, or //[[indeterminates]]//, $x$ and $y$.
+  * This is an equation in two //[[variables]]//, or //[[indeterminates]]//, $x$ and $y$.
+  * A [[solution]] of this equation is a pair of numbers $(a,b)\in \mathbb{R}^2$ so that if we replace $x$ with $a$ and replace $y$ with $b$, then the equation becomes true.
+  * In other words, so that $2a+5b$ really is equal to $7$.
-A [[solution]] of this equation is a pair of numbers $(a,b)\in \mathbb{R}^2$ so that if we replace $x$ with $a$ and replace $y$ with $b$, then the equation becomes true.
+==== $2x+5y=7$ ====
-In other words, so that $2a+5b$ really is equal to $7$.
   * $(3,1)$ is not a solution, because $2\times 3+5\times 1\ne 7$
@@ Line 17: / Line 17: @@
   * Other solutions include $(0,\tfrac 75)$, $(0.5,1.2)$, $(6,-1)$, $(3.5,0)$, $(-\tfrac32,2)$, ...
-We can't make a complete list of all solutions, since there are //infinitely many// solutions in $\mathbb{R}^2$. However, we can draw the set of all solutions as a subset of $\mathbb{R}^2$. This turns out to be a straight line:
+==== $2x+5y=7$ ====
-{{ ::g1.jpg-000.jpg?nolink&600 |}}
-We say that the equation $2x+5y=7$ is a [[linear equation in two variables]].
+  * We can't make a complete list of all solutions, since there are //infinitely many// solutions in $\mathbb{R}^2$. However, we can draw the set of all solutions as a subset of $\mathbb{R}^2$. This turns out to be a straight line
+  * {{::g1.jpg-000.jpg?nolink&600|}}
+  * $2x+5y=7$ is a [[linear equation in two variables]].
@@ Line 29: / Line 30: @@
   * $y-x=1$ {{ ::s-000.jpg?nolink&300 |}}
+==== More examples of linear equations in two variables ====
   * $x-y=0$ {{ ::r-000.jpg?nolink&300 |}}
+==== More examples of linear equations in two variables ====
   * $x=0\iff 1x+0y=0$ {{ ::r-001.jpg?nolink&300 |}}