{"id":1027,"date":"2024-05-05T04:35:30","date_gmt":"2024-05-05T04:35:30","guid":{"rendered":"https:\/\/gbelentzas.sites.sch.gr\/?p=1027"},"modified":"2024-05-13T12:23:18","modified_gmt":"2024-05-13T12:23:18","slug":"%cf%83%ce%b7%ce%bc%ce%b5%ce%af%ce%bf%cf%85-%cf%84%ce%bf%ce%bc%ce%ae%cf%82-%ce%b4%cf%8d%ce%bf-%ce%b5%cf%85%ce%b8%ce%b5%ce%b9%cf%8e%ce%bd","status":"publish","type":"post","link":"https:\/\/gbelentzas.sites.sch.gr\/?p=1027","title":{"rendered":"\u03a3\u03b7\u03bc\u03b5\u03af\u03bf \u03c4\u03bf\u03bc\u03ae\u03c2 \u03b4\u03cd\u03bf \u03b5\u03c5\u03b8\u03b5\u03b9\u03ce\u03bd"},"content":{"rendered":"
\n

<\/i> Math How-To Guide<\/strong><\/span><\/em><\/h4>\n<\/div>\n

\u0394\u03af\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bf\u03b9 \u03b5\u03c5\u03b8\u03b5\u03af\u03b5\u03c2 <\/span>\"\textcolor{blue}{\epsilon_1: (\alpha+\beta)x-2y=12}\" \u03ba\u03b1\u03b9 <\/span>\"\textcolor{blue}{\epsilon_2: x+(6\alpha+2\beta)y=-4}\"<\/p>\n

\u0397 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 <\/span>\"\textcolor{blue}{\epsilon_1}\" \u03c4\u03ad\u03bc\u03bd\u03b5\u03b9 \u03c4\u03bf\u03bd \u03ac\u03be\u03bf\u03bd\u03b1 <\/span>\"\textcolor{blue}{x'x}\" \u03c3\u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03bc\u03b5 \u03c4\u03b5\u03c4\u03bc\u03b7\u03bc\u03ad\u03bd\u03b7 4, \u03b5\u03bd\u03ce \u03b7 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 <\/span>\"\textcolor{blue}{\epsilon_2}\" \u03c4\u03ad\u03bc\u03bd\u03b5\u03b9 \u03c4\u03bf\u03bd \u03ac\u03be\u03bf\u03bd\u03b1 <\/span>\"\textcolor{blue}{y'y}\" \u03c3\u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03bc\u03b5 \u03c4\u03b5\u03c4\u03b1\u03b3\u03bc\u03ad\u03bd\u03b7 -2.<\/span><\/p>\n

\u03b1) \u00a0\u039d\u03b1 \u03b2\u03c1\u03b5\u03af\u03c4\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2 <\/span>\"\textcolor{blue}{\alpha}\" \u03ba\u03b1\u03b9<\/span>\u00a0\"\textcolor{blue}{\beta}.\"<\/p>\n

\u03b2) \u00a0\u039d\u03b1 \u03b2\u03c1\u03b5\u03af\u03c4\u03b5 \u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03c4\u03bf\u03bc\u03ae\u03c2 \u03c4\u03c9\u03bd \u03b5\u03c5\u03b8\u03b5\u03b9\u03ce\u03bd <\/span>\"\textcolor{blue}{\epsilon_1}\" \u03ba\u03b1\u03b9 <\/span>\"\textcolor{blue}{\epsilon_2}.\"<\/p>\n

\u039b\u03cd\u03c3\u03b7<\/strong><\/span><\/h4>\n

\u0393\u03bd\u03c9\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03cc\u03bb\u03b1 \u03c4\u03b1 \u03c3\u03b7\u03bc\u03b5\u03af\u03b1 \u03c4\u03bf\u03c5 \u03ac\u03be\u03bf\u03bd\u03b1 \"x'x\" \u00a0\u03ad\u03c7\u03bf\u03c5\u03bd \u03c4\u03b5\u03c4\u03b1\u03b3\u03bc\u03ad\u03bd\u03b7 0. \u0395\u03c0\u03bf\u03bc\u03ad\u03bd\u03c9, \u03b7 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \"\epsilon_1\" \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 \u03bc\u03b5 \u03c4\u03b5\u03c4\u03bc\u03b7\u03bc\u03ad\u03bd\u03b7 4, \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae \u03c4\u03bf\u03bd \u03c4\u03ad\u03bc\u03bd\u03b5\u03b9 \u03c3\u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u039a(4,0).<\/p>\n

\u0395\u03c6\u03cc\u03c3\u03bf\u03bd \u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u039a(4,0) \u03b1\u03bd\u03ae\u03ba\u03b5\u03b9 \u03c3\u03c4\u03b7\u03bd \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \"\epsilon_1\", \u03c4\u03cc\u03c4\u03b5 \u03bf\u03b9 \u03c3\u03c5\u03bd\u03c4\u03b5\u03c4\u03b1\u03b3\u03bc\u03ad\u03bd\u03b5\u03c2 \u03c4\u03bf\u03c5 \u03b5\u03c0\u03b1\u03bb\u03b7\u03b8\u03b5\u03cd\u03bf\u03c5\u03bd \u03c4\u03b7\u03bd \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1\u03c2. \u0395\u03c0\u03bf\u03bc\u03ad\u03bd\u03c9\u03c2,<\/p>\n

  <\/span>   <\/span>\"\begin{align*}<\/p>\n

H \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \"\epsilon_2\" \u03c4\u03ad\u03bc\u03bd\u03b5\u03b9 \u03c4\u03bf\u03bd \u03ac\u03be\u03bf\u03bd\u03b1 \"y'y\" \u03c3\u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03bc\u03b5 \u03c4\u03b5\u03c4\u03b1\u03b3\u03bc\u03ad\u03bd\u03b7 -2, \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae \u03c3\u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u039b(0,-2), \u03b1\u03c6\u03bf\u03cd \u03cc\u03bb\u03b1 \u03c4\u03b1 \u03c3\u03b7\u03bc\u03b5\u03af\u03b1 \u03c4\u03bf\u03c5 \u03ac\u03be\u03bf\u03bd\u03b1 \"y'y\" \u00a0\u03ad\u03c7\u03bf\u03c5\u03bd \u03c4\u03b5\u03c4\u03bc\u03b7\u03bc\u03ad\u03bd\u03b7 0.<\/p>\n

\u0395\u03c6\u03cc\u03c3\u03bf\u03bd \u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u039b(0,-2) \u03b1\u03bd\u03ae\u03ba\u03b5\u03b9 \u03c3\u03c4\u03b7\u03bd \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \"\epsilon_2\", \u03c4\u03cc\u03c4\u03b5 \u03bf\u03b9 \u03c3\u03c5\u03bd\u03c4\u03b5\u03c4\u03b1\u03b3\u03bc\u03ad\u03bd\u03b5\u03c2 \u03c4\u03bf\u03c5 \u03b5\u03c0\u03b1\u03bb\u03b7\u03b8\u03b5\u03cd\u03bf\u03c5\u03bd \u03c4\u03b7\u03bd \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1\u03c2. \u0395\u03c0\u03bf\u03bc\u03ad\u03bd\u03c9\u03c2,<\/p>\n

  <\/span>   <\/span>\"\begin{align*}<\/p>\n

\u039c\u03c0\u03bf\u03c1\u03bf\u03cd\u03bc\u03b5 \u03bd\u03b1 \u03b1\u03c0\u03bb\u03bf\u03c0\u03bf\u03b9\u03ae\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b7\u03bd \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03b4\u03b9\u03b1\u03b9\u03c1\u03ce\u03bd\u03c4\u03b1\u03c2 \u03ba\u03ac\u03b8\u03b5 \u03cc\u03c1\u03bf \u03bc\u03b5 \u03c4\u03bf 2. \u0394\u03b7\u03bb\u03b1\u03b4\u03ae<\/p>\n

  <\/span>   <\/span>\"\[\dfrac{6\alpha}{2}+\dfrac{2\beta}{2}=\dfrac{2}{2}\]\"<\/p>\n

  <\/span>   <\/span>\"\[3\alpha+\beta=1\]\"<\/p>\n

\u0388\u03c7\u03bf\u03c5\u03bc\u03b5 \u03ba\u03b1\u03c4\u03b1\u03bb\u03ae\u03be\u03b5\u03b9 \u03c3\u03c4\u03bf \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1<\/p>\n

  <\/span>   <\/span>\"\[\left\{\begin{array}{l}\alpha+\beta=3\\3\alpha+\beta=1\end{array}\right.\]\"<\/p>\n

\u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bc\u03b5 \u03bd\u03b1 \u03c4\u03bf \u03bb\u03cd\u03c3\u03bf\u03c5\u03bc\u03b5 \u03bc\u03b5 \u03c4\u03b7 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf \u03c4\u03c9\u03bd \u03b1\u03bd\u03c4\u03af\u03b8\u03b5\u03c4\u03c9\u03bd \u03c3\u03c5\u03bd\u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ce\u03bd \u03ae \u03c4\u03b7 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf \u03c4\u03b7\u03c2 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b1\u03c4\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7\u03c2. \u039c\u03b7 \u03b2\u03b1\u03c1\u03b9\u03ad\u03c3\u03b1\u03b9, \u03bb\u03cd\u03c3\u03c4\u03bf…<\/p>\n

\u039a\u03b1\u03c4\u03b1\u03bb\u03ae\u03b3\u03bf\u03c5\u03bc\u03b5, \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd, \u03cc\u03c4\u03b9 \"\alpha=-1\" \u03ba\u03b1\u03b9 \"\beta=4\".<\/p>\n

\u03b2) \u0393\u03b9\u03b1 \u03bd\u03b1 \u03bb\u03cd\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf \u03b5\u03c1\u03ce\u03c4\u03b7\u03bc\u03b1 \u03b1\u03c5\u03c4\u03cc \u03b8\u03b1 \u03ba\u03ac\u03bd\u03bf\u03c5\u03bc\u03b5 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b1\u03c4\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03c9\u03bd \u03b1 \u03ba\u03b1\u03b9 \u03b2 \u03c0\u03bf\u03c5 \u03b2\u03c1\u03ae\u03ba\u03b1\u03bc\u03b5 \u03c3\u03c4\u03bf \u03b5\u03c1\u03ce\u03c4\u03b7\u03bc\u03b1 \u03b1 \u03c3\u03c4\u03b9\u03c2 \u03b5\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2 \u03c4\u03c9\u03bd \u03b5\u03c5\u03b8\u03b5\u03b9\u03ce\u03bd.<\/p>\n

H \"\gre_1\" \u03b3\u03c1\u03ac\u03c6\u03b5\u03c4\u03b1\u03b9<\/p>\n

  <\/span>   <\/span>\"\begin{align*}<\/p>\n

\u03ba\u03b1\u03b9 \u03b7 \"\gre_2\" \u03b3\u03c1\u03ac\u03c6\u03b5\u03c4\u03b1\u03b9<\/p>\n

  <\/span>   <\/span>\"\begin{align*}<\/p>\n

\u03a4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03c4\u03bf\u03bc\u03ae\u03c2 \u03c4\u03c9\u03bd \u03b5\u03c5\u03b8\u03b5\u03b9\u03ce\u03bd \"\epsilon_1\" \u03ba\u03b1\u03b9 \"\epsilon_2\" \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03bb\u03cd\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c3\u03c5\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2<\/p>\n

  <\/span>   <\/span>\"\[\left\{\begin{array}{l}3x-2y=12\\x+2y=-4\end{array}\right.\]\"<\/p>\n

\u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf …. \u03ad\u03c7\u03b5\u03b9 \u03bb\u03cd\u03c3\u03b7 \u03c4\u03bf (x,y)=(2,-3), \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae \u03c4\u03bf \u03bf\u03b9 \u03b5\u03c5\u03b8\u03b5\u03af\u03b5\u03c2 \u03c4\u03ad\u03bc\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c3\u03c4\u03bf \u00a0\u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u039c(2,-3).<\/p>\n

\u039c\u03b5 \u03c4\u03b7 \u03b2\u03bf\u03ae\u03b8\u03b5\u03b9\u03b1 \u03c4\u03bf\u03c5 Geogebra, \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bc\u03b5 \u03bd\u03b1 \u03b4\u03bf\u03cd\u03bc\u03b5 \u03ba\u03b1\u03b9 \u03c4\u03b7 \u03b3\u03c1\u03b1\u03c6\u03b9\u03ba\u03ae \u03b5\u03c0\u03af\u03bb\u03c5\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c0\u03c1\u03bf\u03b2\u03bb\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2.<\/p>\n

\"\"<\/p>\n

\n
\n

\u00a0<\/i> \u00a0\u03a3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2 \u0398\u03b5\u03c9\u03c1\u03af\u03b1\u03c2<\/span><\/strong><\/em><\/h4>\n
    \n
  • \u0391\u03bd \u03ad\u03bd\u03b1 \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03b1\u03bd\u03ae\u03ba\u03b5\u03b9 \u03c3\u03b5 \u03bc\u03b9\u03b1 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1, \u03c4\u03cc\u03c4\u03b5 \u03bf\u03b9 \u03c3\u03c5\u03bd\u03c4\u03b5\u03c4\u03b1\u03b3\u03bc\u03ad\u03bd\u03b5\u03c2 \u03c4\u03bf\u03c5 \u03b5\u03c0\u03b1\u03bb\u03b7\u03b8\u03b5\u03cd\u03bf\u03c5\u03bd \u03c4\u03b7\u03bd \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1\u03c2.<\/li>\n
  • \u0391\u03bd \u03bf\u03b9 \u03c3\u03c5\u03bd\u03c4\u03b5\u03c4\u03b1\u03b3\u03bc\u03ad\u03bd\u03b5\u03c2 \u03b5\u03bd\u03cc\u03c2 \u03c3\u03b7\u03bc\u03b5\u03af\u03bf\u03c5 \u03b5\u03c0\u03b1\u03bb\u03b7\u03b8\u03b5\u03cd\u03bf\u03c5\u03bd \u03c4\u03b7\u03bd \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03bc\u03b9\u03b1\u03c2 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1\u03c2, \u03c4\u03cc\u03c4\u03b5 \u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03b1\u03bd\u03ae\u03ba\u03b5\u03b9 \u03c3\u03c4\u03b7\u03bd \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \u03b1\u03c5\u03c4\u03ae.<\/li>\n<\/ul>\n
    \n
    \n

    <\/i> Let’s practice<\/strong><\/span><\/em><\/h4>\n<\/div>\n

    \u0386\u03c3\u03ba\u03b7\u03c3\u03b7 1.<\/strong> \u039d\u03b1 \u03b2\u03c1\u03b5\u03af\u03c4\u03b5 \u03c4\u03bf \u03ba\u03bf\u03b9\u03bd\u03cc \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03c4\u03c9\u03bd \u03b5\u03c5\u03b8\u03b5\u03b9\u03ce\u03bd<\/p>\n

    \u03b51<\/sub> : 2x + 5y = 9 \u03ba\u03b1\u03b9 \u03b52<\/sub> : x – y = 1.<\/p>\n

    \u0386\u03c3\u03ba\u03b7\u03c3\u03b7 2.<\/strong> Av \u03bf\u03b9 \u03b5\u03c5\u03b8\u03b5\u03af\u03b5\u03c2 \u03b51<\/sub> : (\u03bb + \u03bc)x + y = 7 \u03ba\u03b1\u03b9\u03b52<\/sub>: x + (\u03bb + 3\u03bc)y = 1 \u03c4\u03ad\u03bc\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c3\u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u0391(2, 1), \u03bd\u03b1 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03c3\u03b5\u03c4\u03b5 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03c9\u03bd \u03bb \u03ba\u03b1\u03b9 \u03bc.<\/p>\n

    \u0386\u03c3\u03ba\u03b7\u03c3\u03b7 3.<\/strong> \u0397 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \u03bc\u03b5 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03b1x + y = \u03b2 \u03b4\u03b9\u03ad\u03c1\u03c7\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03b1 \u03c3\u03b7\u03bc\u03b5\u03af\u03b1 \u0391(1, 2) \u03ba\u03b1\u03b9 \u0392(-3, -2). \u039d\u03b1 \u03b2\u03c1\u03b5\u03af\u03c4\u03b5 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03c9\u03bd \u03b1, \u03b2.<\/p>\n

    \u0386\u03c3\u03ba\u03b7\u03c3\u03b7 4.<\/strong> \u039d\u03b1 \u03b2\u03c1\u03b5\u03b8\u03b5\u03af \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1\u03c2 \u03c0\u03bf\u03c5 \u03b4\u03b9\u03ad\u03c1\u03c7\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03b1 \u03c3\u03b7\u03bc\u03b5\u03af\u03b1 \u0391(2, 3) \u03ba\u03b1\u03b9 \u0392 (4, 1).<\/p>\n

    \u0386\u03c3\u03ba\u03b7\u03c3\u03b7 5.<\/strong> \u0394\u03af\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bf\u03b9 \u03b5\u03c5\u03b8\u03b5\u03af\u03b5\u03c2<\/p>\n

    \u03b51<\/sub> : 2x – 3y = -14, \u00a0\u03b52<\/sub> : x + y = -2 \u03ba\u03b1\u03b9<\/p>\n

    \u03b53<\/sub> : 3x – y = 14<\/p>\n

    \u03b1)<\/strong> \u039d\u03b1 \u03b2\u03c1\u03b5\u03af\u03c4\u03b5 \u03c4\u03bf \u03ba\u03bf\u03b9\u03bd\u03cc \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03c4\u03c9\u03bd \u03b5\u03c5\u03b8\u03b5\u03b9\u03ce\u03bd \u03b51 \u03ba\u03b1\u03b9 \u03b52.<\/p>\n

    \u03b2)<\/strong> \u039d\u03b1 \u03b5\u03be\u03b5\u03c4\u03ac\u03c3\u03b5\u03c4\u03b5 \u03b1\u03bd \u03b7 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \u03b53 \u03b4\u03b9\u03ad\u03c1\u03c7\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03c4\u03bf\u03bc\u03ae\u03c2 \u03c4\u03c9\u03bd \u03b5\u03c5\u03b8\u03b5\u03b9\u03ce\u03bd \u03b51 \u03ba\u03b1\u03b9 \u03b52.<\/p>\n

    \u0386\u03c3\u03ba\u03b7\u03c3\u03b7 6.<\/strong>\u00a0\u0394\u03af\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bf\u03b9 \u03b5\u03c5\u03b8\u03b5\u03af\u03b5\u03c2<\/p>\n

    \"\epsilon_1: 3x-y=1\" \u03ba\u03b1\u03b9<\/p>\n

    \"\epsilon_2: 5x+2y=9\"<\/p>\n

    \u03b1)<\/strong> \u039d\u03b1 \u03b2\u03c1\u03b5\u03af\u03c4\u03b5 \u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03c4\u03bf\u03bc\u03ae\u03c2 \u03c4\u03c9\u03bd \u03b5\u03c5\u03b8\u03b5\u03af\u03c9\u03bd \"\epsilon_1\" \u03ba\u03b1\u03b9 \"\epsilon_2.\"<\/p>\n

    \u03b2)<\/strong> \u0391\u03bd \u03b7 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 <\/p>\n

      <\/span>   <\/span>\"\[\epsilon_3: (\alpha+1)^2x+(\alpha+4)y=3-\alpha\]\"<\/p>\n

    \u03b4\u03b9\u03ad\u03c1\u03c7\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03c4\u03bf\u03bc\u03ae\u03c2 \u03c4\u03c9\u03bd \"\epsilon_1\" \u03ba\u03b1\u03b9 \"\epsilon_2,\" \u03bd\u03b1 \u03b2\u03c1\u03b5\u03af\u03c4\u03b5 \u03c4\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \"\alpha.\"<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

    Math How-To Guide \u0394\u03af\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bf\u03b9 \u03b5\u03c5\u03b8\u03b5\u03af\u03b5\u03c2 \u03ba\u03b1\u03b9 \u0397 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \u03c4\u03ad\u03bc\u03bd\u03b5\u03b9 \u03c4\u03bf\u03bd \u03ac\u03be\u03bf\u03bd\u03b1 \u03c3\u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03bc\u03b5 \u03c4\u03b5\u03c4\u03bc\u03b7\u03bc\u03ad\u03bd\u03b7 4, \u03b5\u03bd\u03ce \u03b7 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1 \u03c4\u03ad\u03bc\u03bd\u03b5\u03b9 \u03c4\u03bf\u03bd \u03ac\u03be\u03bf\u03bd\u03b1 \u03c3\u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03bc\u03b5 \u03c4\u03b5\u03c4\u03b1\u03b3\u03bc\u03ad\u03bd\u03b7 -2. \u03b1) \u00a0\u039d\u03b1 \u03b2\u03c1\u03b5\u03af\u03c4\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2 \u03ba\u03b1\u03b9\u00a0 \u03b2) \u00a0\u039d\u03b1 \u03b2\u03c1\u03b5\u03af\u03c4\u03b5 \u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03c4\u03bf\u03bc\u03ae\u03c2 \u03c4\u03c9\u03bd \u03b5\u03c5\u03b8\u03b5\u03b9\u03ce\u03bd \u03ba\u03b1\u03b9 \u039b\u03cd\u03c3\u03b7 \u0393\u03bd\u03c9\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03cc\u03bb\u03b1 \u03c4\u03b1 \u03c3\u03b7\u03bc\u03b5\u03af\u03b1 \u03c4\u03bf\u03c5…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-1027","post","type-post","status-publish","format-standard","hentry","category-3---"],"featured_image_src":null,"author_info":{"display_name":"admin","author_link":"https:\/\/gbelentzas.sites.sch.gr\/?author=1"},"yoast_head":"\n\u03a3\u03b7\u03bc\u03b5\u03af\u03bf \u03c4\u03bf\u03bc\u03ae\u03c2 \u03b4\u03cd\u03bf \u03b5\u03c5\u03b8\u03b5\u03b9\u03ce\u03bd - 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