B\u0130R\u0130NC\u0130 DERECEDEN B\u0130R B\u0130L\u0130NMEYENL\u0130 DENKLEMLER<\/p>\n
A. TANIM<\/p>\n
a ve b ger\u00e7el (reel) say\u0131lar ve a \u00b9 0 olmak \u00fczere,
\nax + b = 0 e\u015fitli\u011fine birinci dereceden bir bilinmeyenli denklem denir.
\n Bu denklemi sa\u011flayan x de\u011ferlerine denklemin k\u00f6k\u00fc, denklemin k\u00f6k\u00fcn\u00fcn olu\u015fturdu\u011fu k\u00fcmeye denklemin \u00e7\u00f6z\u00fcm k\u00fcmesi denir.
\nB. E\u015e\u0130TL\u0130\u011e\u0130N \u00d6ZELL\u0130KLER\u0130<\/p>\n
1) a = b ise, a \u00b1 c = b \u00b1 c dir.
\n2) a = b ise, a . c = b . c dir.
\n3) a = b ise,
\n4) a = b ise, an = bn dir.
\n5) a = b ise,
\n6) (a = b ve b = c) ise, a = c dir.\u00dc
\n7) (a = b ve c = d) ise, a \u00b1 c = b \u00b1 d
\n8) (a = b ve c = d) ise, a . c = b . d dir.
\n9) (a = b ve c = d) ise,
\n10) a . b = 0 ise, (a = 0 veya b = 0) d\u0131r.
\n11) a . b \u00b9 0 ise, (a \u00b9 0 ve b \u00b9 0) d\u0131r.
\n12) = 0 ise, (a = 0 ve b \u00b9 0) d\u0131r.<\/p>\n
C. ax + b = 0 DENKLEM\u0130N\u0130N \u00c7\u00d6Z\u00dcM K\u00dcMES\u0130
\na \u00b9 0 olmak \u00fczere,
\n ax + b = 0 ise,
\n(a = 0 ve b = 0) ise, ax + b = 0 denklemini b\u00fct\u00fcn say\u0131lar sa\u011flar. Buna g\u00f6re, reel (ger\u00e7el) say\u0131larda \u00e7\u00f6z\u00fcm k\u00fcmesi IR dir.
\n(a = 0 ve b \u00b9 0) ise, ax + b = 0 denklemini sa\u011flayan hi\u00e7bir say\u0131 yoktur.
\n Yani, \u00c7 = \u00c6 dir.
\nD. B\u0130R\u0130NC\u0130 DERECEDEN \u0130K\u0130 B\u0130L\u0130NMEYENL\u0130 DENKLEM S\u0130STEM\u0130<\/p>\n
a, b, c \u00ce IR, a \u00b9 0 ve b \u00b9 0 olmak \u00fczere,
\n ax + by + c = 0 denklemine birinci dereceden iki bilinmeyenli denklem denir.
\n Bu denklem d\u00fczlemde bir do\u011fru belirtir. Do\u011fru \u00fczerindeki b\u00fct\u00fcn noktalar\u0131n olu\u015fturdu\u011fu ikililer denkle-min \u00e7\u00f6z\u00fcm k\u00fcmesidir.
\n Buna g\u00f6re, ax + by + c = 0 denkleminin \u00e7\u00f6z\u00fcm k\u00fcmesi bir\u00e7ok ikiliden olu\u015fur.
\na, b, c \u00ce IR olmak \u00fczere,<\/p>\n
ax + by + c = 0
\ndenklemi her (x, y) \u00ce IR2 i\u00e7in sa\u011flan\u0131yorsa<\/p>\n
a = b = c = 0 d\u0131r.
\nBirden fazla iki bilinmeyenli denklemden olu\u015fan sisteme birinci dereceden iki bilinmeyenli denklem sistemi denir.
\n\u00c7\u00f6z\u00fcm K\u00fcmesinin Bulunmas\u0131
\n Birinci dereceden iki bilinmeyenli denklem sistemlerinin \u00e7\u00f6z\u00fcm k\u00fcmesi; yok etme y\u00f6ntemi, yerine koyma y\u00f6ntemi, grafik y\u00f6ntemi, determinant y\u00f6ntemi gibi y\u00f6ntemlerden biri ile yap\u0131l\u0131r.
\nBiz burada \u00fc\u00e7\u00fcn\u00fc verece\u011fiz.
\na. Yok Etme Y\u00f6ntemi: De\u011fi\u015fkenlerden biri yok edilecek bi\u00e7imde verilen denklem sistemi d\u00fczenlenir ve taraf tarafa toplan\u0131r.
\n Taraf tarafa topland\u0131\u011f\u0131nda veya \u00e7\u0131kar\u0131ld\u0131\u011f\u0131nda (ya da bir d\u00fczenlemeden sonra) de\u011fi\u015fkenlerden biri sadele\u015fiyorsa \u201cYok etme y\u00f6ntemi\u201d kolayl\u0131k sa\u011flar.
\nb. Yerine Koyma Y\u00f6ntemi: Verilen denklemlerin birinden, de\u011fi\u015fkenlerden biri \u00e7ekilip di\u011fer denklem-de yerine yaz\u0131larak sonuca gidilir.
\n Denklemlerin birinden, de\u011fi\u015fkenlerden biri kolayca \u00e7ekilebiliyorsa, \u201cYerine koyma y\u00f6ntemi\u201d kolayl\u0131k sa\u011flar.
\nc. Kar\u015f\u0131la\u015ft\u0131rma Y\u00f6ntemi: Verilen denklemlerin iki-sinden de ayn\u0131 de\u011fi\u015fken \u00e7ekilir. Denklemlerin di\u011fer taraflar\u0131 kar\u015f\u0131la\u015ft\u0131r\u0131l\u0131r (e\u015fitlenir).
\n Her iki denklemden de ayn\u0131 de\u011fi\u015fken kolayca \u00e7ekilebiliyorsa, \u201cKar\u015f\u0131la\u015ft\u0131rma y\u00f6ntemi\u201d kolayl\u0131k sa\u011flar.
\n\u00dc ax + by + c = 0
\n dx + ey + f = 0
\n denklem sistemini g\u00f6z \u00f6n\u00fcne alal\u0131m:
\n Bu iki denklemin her birinin d\u00fczlemde bir do\u011fru belirtti\u011fi g\u00f6z \u00f6n\u00fcne al\u0131n\u0131rsa \u00fc\u00e7 durum oldu\u011fu g\u00f6r\u00fcl\u00fcr.
\nBirinci durum:
\nise, bu iki do\u011fru tek bir noktada kesi\u015fir.
\n Verilen denklem sisteminin \u00e7\u00f6z\u00fcm k\u00fcmesi bir tek noktadan olu\u015fur.
\n\u0130kinci durum:
\n ise, bu iki do\u011fru \u00e7ak\u0131\u015f\u0131kt\u0131r.
\n Do\u011fru \u00fczerindeki her nokta denklem sistemini sa\u011flar.
\n Verilen denklem sisteminin \u00e7\u00f6z\u00fcm k\u00fcmesi sonsuz noktadan olu\u015fur.
\n\u00dc\u00e7\u00fcnc\u00fc durum:
\nise, bu iki do\u011fru paraleldir.
\n Denklem sistemini sa\u011flayan hi\u00e7bir nokta bulunamaz.
\n Verilen denklem sisteminin \u00e7\u00f6z\u00fcm k\u00fcmesi bo\u015f k\u00fcmedir.<\/p>\n","protected":false},"excerpt":{"rendered":"
B\u0130R\u0130NC\u0130 DERECEDEN B\u0130R B\u0130L\u0130NMEYENL\u0130 DENKLEMLER A. TANIM a ve b ger\u00e7el (reel) say\u0131lar ve a \u00b9 0 olmak \u00fczere, ax + b = 0 e\u015fitli\u011fine birinci dereceden bir bilinmeyenli denklem denir. Bu denklemi sa\u011flayan x de\u011ferlerine denklemin k\u00f6k\u00fc, denklemin k\u00f6k\u00fcn\u00fcn olu\u015fturdu\u011fu k\u00fcmeye denklemin \u00e7\u00f6z\u00fcm k\u00fcmesi denir. B. E\u015e\u0130TL\u0130\u011e\u0130N \u00d6ZELL\u0130KLER\u0130 1) a = b ise, a …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1404,1403],"tags":[7289,7291,7290],"class_list":["post-3092","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-birinci-dereceden-bir-bilinmeyenli-denklemler","tag-denklem-sistemi","tag-reel-gercel-sayilar"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3092","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=3092"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3092\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3092"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3092"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3092"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}