vault backup: 2022-05-09 09:20:04

notes/.obsidian/plugins/obsidian-activity-history/data.json

@@ -12,8 +12,8 @@
   "checkpointList": [
     {
       "path": "/",
-      "date": "2022-05-06",
-      "size": 835468
+      "date": "2022-05-09",
+      "size": 835273
     }
   ],
   "activityHistory": [
@@ -639,6 +639,10 @@
         {
           "date": "2022-05-06",
           "value": 1296
+        },
+        {
+          "date": "2022-05-09",
+          "value": 655
         }
       ]
     }

notes/mat/Rovnice/Soustavy rovnic.md

@@ -50,56 +50,43 @@ $3xy-19y=30$
 
 $5x+3(y+2)=20$
 $5x+3y=14$
+$x=\frac{14-3y}5$
 
-$9y^2+5y-26=0$
-$D=b^2-4ac$
-$D=5^2-4*9*(-26)$
-$D=25+936$
-$D=961$
-$\sqrt{D}=31$
-$y_{1;2}=\frac{-b\pm\sqrt{D}}{2a}$
-$y_1=\frac{-5+31}{2*9}=\frac{13}9$
-$y_2=\frac{-5-31}{2*9}=-2$
+$3(\frac{14-3y}5)-\frac4{y-2}=13$
+$\frac{42-9y}5-\frac4{y-2}-13=2$
 
-$5x+3(y+2)=20$
-$5x+3(-2+2)=20$
-$5x=20$
-$x=4$
+$x_1=\frac{14}5-\frac35$
+$x_1=4$
+$x_2=\frac{14}5-\frac35*\frac{13}9$
+$x_2=\frac{29}{15}$
 
-$5x+3(y+2)=20$
-$5x+3(\frac{13}9+2)=20$
-$5x+\frac{39}9+2=20$
-$5x+6+\frac13=20$
-$5x+\frac13=14$
-$5x=14-\frac13$
-$x=\frac{41}{15}$
+$\frac{-23(y-2)-9y(y-2)-20}{5y-2}=0$
+$-5y+26-9y^2=0$
+$(y+2)(9y-13)=0$
+$y_1=-2$
+$y_2=\frac{13}9$
+
+$K=\{(-2;4);(\frac{13}9;\frac{29}{15})\}$
 
 ## B (substituční)
 
 $\frac{x-1}8-\frac{y-7}4=1$
 $2x+\frac{2y-5}3 = 21$
 
-$x-1-2{y-7}=8$
-$x-8-2y=8$
-$x-2y=16$
-$x=16+2y$
-$x=16+2(34-3x)$
-$x=16+2(34-3(16+2(34-3(16+2y))))$
-$x=16+2(\frac{14}5)$
-$x=16+\frac{28}5$
-$x=16+5.6$
-$x=21.6$
+$\frac{x-1}8-\frac{y-7}4=1$
 
-$2x+\frac{2y-5}3 = 21$
-$6x+2y-5 = 63$
-$6x+2y=68$
-$2y=68-6x$
-$y=34-3(16+2y)$
-$y=34-48+6y$
-$y=-14+6y$
-$-5y=-14$
-$5y=14$
-$y=\frac{14}5$
+$2x+\frac{2y-5}3=21$
+$x=\frac{21}2-\frac{2y-5}6$
+$x=\frac{63-2y+5}6$
+$x=\frac{2(34-y)}6$
+$x=\frac{34-y}3$
+
+$\frac{\frac{34-y}3-1}8-\frac{y-7}4=1$
+
+$y=7$
+$x=\frac{34-7}3$
+$x=9$
+$K=\{(9;7)\}$
 
 ## C (srovnávací)