{"id":1154,"date":"2024-09-08T18:30:03","date_gmt":"2024-09-08T18:30:03","guid":{"rendered":"https:\/\/gbelentzas.sites.sch.gr\/?p=1154"},"modified":"2024-09-10T17:26:30","modified_gmt":"2024-09-10T17:26:30","slug":"1-1-%ce%b3%cf%81%ce%b1%ce%bc%ce%bc%ce%b9%ce%ba%ce%b1-%cf%83%cf%85%cf%83%cf%84%ce%b7%ce%bc%ce%b1%cf%84%ce%b1-%ce%b7-%ce%b5%ce%be%ce%af%cf%83%cf%89%cf%83%ce%b7-%ce%b1x-%ce%b2y-%ce%b3-%ce%b8%ce%b5","status":"publish","type":"post","link":"https:\/\/gbelentzas.sites.sch.gr\/?p=1154","title":{"rendered":"1.1 \u0397 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03b1x + \u03b2y = \u03b3 (\u0398\u03b5\u03c9\u03c1\u03af\u03b1)"},"content":{"rendered":"

<\/p>\n

<\/i> \u03a3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2 \u0398\u03b5\u03c9\u03c1\u03af\u03b1\u03c2<\/span><\/em><\/strong><\/h4>\n

\u03a4\u03b9 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03c5\u03bc\u03b5 \u03b3\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ae \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03bc\u03b5 \u03b4\u03cd\u03bf \u03b1\u03b3\u03bd\u03ce\u03c3\u03c4\u03bf\u03c5\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b9 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03c5\u03bc\u03b5 \u03bb\u03cd\u03c3\u03b7 \u03c4\u03b7\u03c2;<\/strong><\/span><\/p>\n

<\/p>\n

\u039a\u03ac\u03b8\u03b5 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03bc\u03bf\u03c1\u03c6\u03ae\u03c2:<\/p>\n

\n

  <\/span>   <\/span>\"\[\alpha x + \beta y = \gamma\]\"<\/p>\n<\/p>\n

\u03bb\u03ad\u03b3\u03b5\u03c4\u03b1\u03b9 \u03b3\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ae \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7<\/strong>. \u0391\u03bd \"\alpha \neq 0\" \u03ae \"\beta \neq 0\" \u03c4\u03cc\u03c4\u03b5 \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c0\u03b1\u03c1\u03b9\u03c3\u03c4\u03ac\u03bd\u03b5\u03b9 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \u03b3\u03c1\u03b1\u03bc\u03bc\u03ae<\/strong>.
\n\u039b\u03cd\u03c3\u03b7<\/strong> \u03c4\u03b7\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7\u03c2 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03c5\u03bc\u03b5 \u03ba\u03ac\u03b8\u03b5 \u03b6\u03b5\u03cd\u03b3\u03bf\u03c2 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \"(x, y)\" \u03c0\u03bf\u03c5 \u03c4\u03b7\u03bd \u03b5\u03c0\u03b1\u03bb\u03b7\u03b8\u03b5\u03cd\u03b5\u03b9.<\/p>\n

\n

\u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7<\/span><\/strong><\/p>\n

\u039d\u03b1 \u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b7 \u03b3\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ae \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 <\/p>\n

  <\/span>   <\/span>\"\[\alpha x + \beta y = \gamma\]\"<\/p>\n

\u03bc\u03b5 \"\alpha \neq 0\" \u03ae \"\beta \neq 0\" \u03c0\u03b1\u03c1\u03b9\u03c3\u03c4\u03ac\u03bd\u03b5\u03b9 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1.<\/p>\n

<\/p>\n

\u0394\u03b9\u03b1\u03ba\u03c1\u03af\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03b5\u03be\u03ae\u03c2 \u03c0\u03b5\u03c1\u03b9\u03c0\u03c4\u03ce\u03c3\u03b5\u03b9\u03c2:<\/p>\n

\u03a0\u03b5\u03c1\u03af\u03c0\u03c4\u03c9\u03c3\u03b7 1:<\/strong> \u0388\u03c3\u03c4\u03c9 \"\beta \neq 0\" \u03ba\u03b1\u03b9 \"\alpha \neq 0\". \u03a4\u03cc\u03c4\u03b5 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5:<\/p>\n

\n

  <\/span>   <\/span>\"\[\alpha x + \beta y = \gamma \Leftrightarrow\]\"<\/p>\n<\/p>\n

\n

  <\/span>   <\/span>\"\[\beta y = -\alpha x + \gamma \Leftrightarrow\]\"<\/p>\n<\/p>\n

\n

  <\/span>   <\/span>\"\[y = -\dfrac{\alpha}{\beta}x + \dfrac{\gamma}{\beta}\]\"<\/p>\n<\/p>\n

A\u03bd \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03af\u03c3\u03bf\u03c5\u03bc\u03b5 \"\lambda = -\dfrac{\alpha}{\beta}\" \u00a0\u03ba\u03b1\u03b9 \u03bc\u03b5 \"\kappa = \dfrac{\gamma}{\beta} \right)\" \u03c4\u03cc\u03c4\u03b5 \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03b3\u03c1\u03ac\u03c6\u03b5\u03c4\u03b1\u03b9 \"y= \lambda x +\kappa\" \u03bc\u03b5 \"\lambda, \kappa\" \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2.<\/p>\n

\u0397 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \"y= \lambda x +\kappa\" \u03c0\u03b1\u03c1\u03b9\u03c3\u03c4\u03ac\u03bd\u03b5\u03b9 \u03bc\u03b9\u03b1 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \u03c0\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03b1\u03c1\u03ac\u03bb\u03bb\u03b7\u03bb\u03b7 \u03c3\u03c4\u03bf\u03bd \u03ac\u03be\u03bf\u03bd\u03b1 x\u0384x \u03ba\u03b1\u03b9 \u03c4\u03ad\u03bc\u03bd\u03b5\u03b9 \u03c4\u03bf\u03bd \u03ac\u03be\u03bf\u03bd\u03b1 y\u0384y \u03c3\u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \"(0, \kappa)\". To \"\lambda\" \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c5\u03bd\u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ae\u03c2 \u03b4\u03b9\u03b5\u03cd\u03b8\u03c5\u03bd\u03c3\u03b7\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1\u03c2.<\/p>\n

\"Rendered<\/p>\n

\u03a0\u03b5\u03c1\u03af\u03c0\u03c4\u03c9\u03c3\u03b7 2:<\/strong> \u0388\u03c3\u03c4\u03c9 \"\beta \neq 0\" \u03ba\u03b1\u03b9 \"\alpha = 0\". \u03a4\u03cc\u03c4\u03b5 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5:<\/p>\n

\n

  <\/span>   <\/span>\"\[\alpha x + \beta y = \gamma \Leftrightarrow 0x + \beta y = \gamma \Leftrightarrow \beta y = \gamma \Leftrightarrow y = \dfrac{\gamma}{\beta}\]\"<\/p>\n<\/p>\n

A\u03bd \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03af\u03c3\u03b6\u03bf\u03c5\u03bc\u03b5 \"\kappa= \dfrac{\gamma}{\beta}\" \u03c4\u03cc\u03c4\u03b5 \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03b3\u03c1\u03ac\u03c6\u03b5\u03c4\u03b1\u03b9 \"y= \kappa\" \u03bc\u03b5 \"\kappa\" \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc.<\/p>\n

    \n
  • \u0391\u03bd \"\kappa\neq 0,\" \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \"y = \kappa\" \u03c0\u03b1\u03c1\u03b9\u03c3\u03c4\u03ac\u03bd\u03b5\u03b9 \u03bc\u03b9\u03b1 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \u03c0\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03b1\u03c1\u03ac\u03bb\u03bb\u03b7\u03bb\u03b7 \u03c3\u03c4\u03bf\u03bd \u03ac\u03be\u03bf\u03bd\u03b1 x\u0384x \u03ba\u03b1\u03b9 \u03c4\u03ad\u03bc\u03bd\u03b5\u03b9 \u03c4\u03bf\u03bd \u03ac\u03be\u03bf\u03bd\u03b1 y\u0384y \u03c3\u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \"(0, \kappa)\" (\u03b2\u03bb. \u03c3\u03c7\u03ae\u03bc\u03b1 1)<\/em><\/strong><\/li>\n
  • \u0395\u03b9\u03b4\u03b9\u03ba\u03cc\u03c4\u03b5\u03c1\u03b1, \u03b1\u03bd \"\kappa=0,\" \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \"y = \kappa\" \u03b3\u03c1\u03ac\u03c6\u03b5\u03c4\u03b1\u03b9 \"y = 0\" \u03ba\u03b1\u03b9 \u03b7 \u03b3\u03c1\u03b1\u03c6\u03b9\u03ba\u03ae \u03c4\u03b7\u03c2 \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf \u03ac\u03be\u03bf\u03bd\u03b1\u03c2 x\u0384x. (\u03b2\u03bb. \u03c3\u03c7\u03ae\u03bc\u03b1 2)<\/em><\/strong><\/li>\n<\/ul>\n

    \"Rendered<\/p>\n

    (\u03a3\u03c7\u03ae\u03bc\u03b1 1)<\/em><\/strong><\/p>\n

    \"Rendered<\/p>\n

    (\u03a3\u03c7\u03ae\u03bc\u03b1 2)<\/em><\/strong><\/p>\n

    \u03a0\u03b5\u03c1\u03af\u03c0\u03c4\u03c9\u03c3\u03b7 3:<\/strong> \u0388\u03c3\u03c4\u03c9 \"\beta = 0\" \u03ba\u03b1\u03b9 \"\alpha \neq 0\". \u03a4\u03cc\u03c4\u03b5 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5:<\/p>\n

    \n

      <\/span>   <\/span>\"\[\alpha x + \beta y = \gamma \Leftrightarrow \alpha x = \gamma \Leftrightarrow x = \dfrac{\gamma}{\alpha}\]\"<\/p>\n<\/p>\n

    A\u03bd \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03af\u03c3\u03b6\u03bf\u03c5\u03bc\u03b5 \"\kappa= \dfrac{\gamma}{\alpha}\" \u03c4\u03cc\u03c4\u03b5 \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03b3\u03c1\u03ac\u03c6\u03b5\u03c4\u03b1\u03b9\u00a0\"x= \kappa\" \u03bc\u03b5 \"\kappa\" \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc.<\/p>\n

      \n
    • \u0391\u03bd \"\kappa\neq 0,\" \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \"x = \kappa\" \u03c0\u03b1\u03c1\u03b9\u03c3\u03c4\u03ac\u03bd\u03b5\u03b9 \u03bc\u03b9\u03b1 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \u03c0\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03b1\u03c1\u03ac\u03bb\u03bb\u03b7\u03bb\u03b7 \u03c3\u03c4\u03bf\u03bd \u03ac\u03be\u03bf\u03bd\u03b1 \"y'y\" \u03ba\u03b1\u03b9 \u03c4\u03ad\u03bc\u03bd\u03b5\u03b9 \u03c4\u03bf\u03bd \u03ac\u03be\u03bf\u03bd\u03b1 \"x'x\" \u03c3\u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \"(\kappa,0)\" (\u03b2\u03bb. \u03c3\u03c7\u03ae\u03bc\u03b1 1)<\/em><\/strong><\/li>\n
    • \u0391\u03bd \"\kappa=0,\" \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \"x = \kappa\" \u03b3\u03c1\u03ac\u03c6\u03b5\u03c4\u03b1\u03b9 \"x = 0\" \u03ba\u03b1\u03b9 \u03b7 \u03b3\u03c1\u03b1\u03c6\u03b9\u03ba\u03ae \u03c4\u03b7\u03c2 \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf \u03ac\u03be\u03bf\u03bd\u03b1\u03c2 \"y'y.\" (\u03b2\u03bb. \u03c3\u03c7\u03ae\u03bc\u03b1 2)<\/em><\/strong><\/li>\n<\/ul>\n

      \"Rendered<\/p>\n

      (\u03a3\u03c7\u03ae\u03bc\u03b1 1)<\/em><\/strong><\/p>\n

      \"Rendered<\/p>\n

      (\u03a3\u03c7\u03ae\u03bc\u03b1 2)<\/em><\/strong><\/p>\n

      \u03a0\u03b1\u03c1\u03b1\u03c4\u03ae\u03c1\u03b7\u03c3\u03b7<\/strong>:<\/em> \u0397 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \"x = k\" \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03b3\u03c1\u03b1\u03c6\u03b9\u03ba\u03ae \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7\u03c2.<\/p>\n

      \n

      <\/p>\n

      \u0392\u03b9\u03b2\u03bb\u03b9\u03bf\u03b3\u03c1\u03b1\u03c6\u03af\u03b1:<\/strong> \u0386\u03bb\u03b3\u03b5\u03b2\u03c1\u03b1 \u0392’ \u039b\u03c5\u03ba\u03b5\u03af\u03bf\u03c5, \u03a3. \u0391\u03bd\u03b4\u03c1\u03b5\u03b1\u03b4\u03ac\u03ba\u03b7\u03c2, \u0392. \u039a\u03b1\u03c4\u03c3\u03b1\u03c1\u03b3\u03cd\u03c1\u03b7\u03c2, \u03a3. \u03a0\u03b1\u03c0\u03b1\u03c3\u03c4\u03b1\u03c5\u03c1\u03af\u03b4\u03b7\u03c2, \u0393. \u03a0\u03bf\u03bb\u03cd\u03b6\u03bf\u03c2, \u0391. \u03a3\u03b2\u03b5\u03c1\u03ba\u03bf\u03c2, \u03a5\u03c0\u03bf\u03c5\u03c1\u03b3\u03b5\u03af\u03bf \u03a0\u03b1\u03b9\u03b4\u03b5\u03af\u03b1\u03c2, \u0388\u03c1\u03b5\u03c5\u03bd\u03b1\u03c2 \u03ba\u03b1\u03b9 \u0398\u03c1\u03b7\u03c3\u03ba\u03b5\u03c5\u03bc\u03ac\u03c4\u03c9\u03bd<\/small><\/p>\n","protected":false},"excerpt":{"rendered":"

      \u03a3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2 \u0398\u03b5\u03c9\u03c1\u03af\u03b1\u03c2 \u03a4\u03b9 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03c5\u03bc\u03b5 \u03b3\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ae \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03bc\u03b5 \u03b4\u03cd\u03bf \u03b1\u03b3\u03bd\u03ce\u03c3\u03c4\u03bf\u03c5\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b9 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03c5\u03bc\u03b5 \u03bb\u03cd\u03c3\u03b7 \u03c4\u03b7\u03c2; \u039a\u03ac\u03b8\u03b5 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03bc\u03bf\u03c1\u03c6\u03ae\u03c2:     \u03bb\u03ad\u03b3\u03b5\u03c4\u03b1\u03b9 \u03b3\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ae \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7. \u0391\u03bd \u03ae \u03c4\u03cc\u03c4\u03b5 \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c0\u03b1\u03c1\u03b9\u03c3\u03c4\u03ac\u03bd\u03b5\u03b9 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \u03b3\u03c1\u03b1\u03bc\u03bc\u03ae. \u039b\u03cd\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7\u03c2 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03c5\u03bc\u03b5 \u03ba\u03ac\u03b8\u03b5 \u03b6\u03b5\u03cd\u03b3\u03bf\u03c2 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03c0\u03bf\u03c5 \u03c4\u03b7\u03bd \u03b5\u03c0\u03b1\u03bb\u03b7\u03b8\u03b5\u03cd\u03b5\u03b9. \u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 \u039d\u03b1 \u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b7 \u03b3\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ae \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7    …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[],"class_list":["post-1154","post","type-post","status-publish","format-standard","hentry","category-1-"],"featured_image_src":null,"author_info":{"display_name":"admin","author_link":"https:\/\/gbelentzas.sites.sch.gr\/?author=1"},"yoast_head":"\n1.1 \u0397 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03b1x + \u03b2y = \u03b3 (\u0398\u03b5\u03c9\u03c1\u03af\u03b1) - 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