Hvordan løse likningssett grafisk

Her skal du lære å løse et likningssett grafisk ved hjelp av en oppskrift som alltid vil ta deg i mål!

Regel

Oppskrift for grafisk løsning

1.

Løs begge likningene for

y

. Det vil si at du skal ha

y

alene på venstre side i begge uttrykkene. Det ser slik ut:

y = a x + b .

2.

Uttrykkene dine er nå lineære funksjoner. Tegn dem i samme koordinatsystem.

3.

Les av skjæringspunktet, et tall fra

x

-aksen og et tall fra

y

-aksen.

Eksempel 1

Løs likningssettet

\begin{align} y - 2 x = 2 (1) 4 y + 4 x & = 20 & (2)1. Først løser du (1) med hensyn til y : y = 2 x + 2 . Deretter løser du (2) med hensyntil y : \begin{array}{l} 4 y + 4 x & = 20 \\ 4 y & = - 4 x + 20 | : 4 \\ y & = - x + 5 \end{array} 2. Tegn grafene til uttrykkene for y i forrige punkt: 3. Les av skjæringspunktet x = 1 og y = 4 .          Skriv svaret slik: SVAR: (x, y) = (1, 4)Husk at det finnes tre ulike varianter for en løsning. Det er varianter der grafene ikke skjærer hverandre, varianter der grafene skjærer hverandre, og varianter der grafene ligger oppå hverandre.Dersom du blir usikker på løsningene du finner ved regning, kan du alltid få en fin oversikt ved å tegne grafene til likningene. Jeg føler ofte at det hjelper å ha et bilde på hvordan det hele henger sammen. Med litt trening vil du oppleve at du kan lage en skisse av disse i hodet. Det er veldig nyttig!Vil du vite mer? Registrer deg Det er gratis!Forrige oppslag Hvordan fremstille likningssett grafisk Neste oppslag Hvordan løse likningssett med innsettingsmetodenTilbakeHjem All matte Spill Statistikk ChatOm oss Om House of Math Om ansatte Karriere Media Foredrag Blogg Kontakt support@houseofmath.com Booking av privatundervisning +47 22 150 300 Adresse Bygdøy allé 23
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            Norge FAQ Lenker ViTarAnsvar Mattemagi for Ukraina Privatundervisning Bootcamps Juniormatte Drillhefter Oppslagsverk Språk English Українська Vilkår Personvern{"props":{"pageProps":{"campaign":false,"topic":{"key":"content/no/encyclopedia/02 Algebra/02 Likninger og ulikheter/01 Likninger/04 Likningssett/403LikningssettGrafiskOppskrift.tex","title":"Hvordan løse likningssett grafisk","metaDescription":"Lær å løse ligningssett grafisk. Oppskriften her vil alltid ta deg i mål!","previewUrl":"https://images.houseofmath.com/eyJrZXkiOiJvdmVybGVhZi1hc3NldHMvcHJldmlldy80MDNsaWtuaW5nc3NldHRncmFmaXNrb3Bwc2tyaWZ0LnBuZyIsImJ1Y2tldCI6ImhvbS1mcm9udGVuZC1hc3NldHMiLCJ2ZXJzaW9uIjozfQ==","path":"/encyclopedia/algebra/likninger-og-ulikheter/likninger/likningssett/hvordan-lose-likningssett-grafisk","language":"no","taskReference":null,"siblings":[{"h1":"Hva er et likningssett?","path":"/encyclopedia/algebra/likninger-og-ulikheter/likninger/likningssett/hva-er-et-likningssett"},{"h1":"Hvordan fremstille likningssett grafisk","path":"/encyclopedia/algebra/likninger-og-ulikheter/likninger/likningssett/hvordan-fremstille-likningssett-grafisk"},{"h1":"Hvordan løse likningssett grafisk","path":"/encyclopedia/algebra/likninger-og-ulikheter/likninger/likningssett/hvordan-lose-likningssett-grafisk"},{"h1":"Hvordan løse likningssett med innsettingsmetoden","path":"/encyclopedia/algebra/likninger-og-ulikheter/likninger/likningssett/hvordan-lose-likningssett-med-innsettingsmetoden"},{"h1":"Hvordan løse likningssett med addisjonsmetoden","path":"/encyclopedia/algebra/likninger-og-ulikheter/likninger/likningssett/hvordan-lose-likningssett-med-addisjonsmetoden"},{"h1":"Hvordan løse ikke-lineære likningssett","path":"/encyclopedia/algebra/likninger-og-ulikheter/likninger/likningssett/hvordan-lose-ikke-lineaere-likningssett"},{"h1":"Hvordan løse likningssett med flere ukjente","path":"/encyclopedia/algebra/likninger-og-ulikheter/likninger/likningssett/hvordan-lose-likningssett-med-flere-ukjente"}],"isRootPath":false,"locale":"no","cssUrl":"/80bd8b3e-74e6-41e8-a473-0237fd221bbf-no-3.css","htmlContent":{"html":" \u003c/p\u003e\u003cp class=\"indent\" \u003e     Her skal du lære å løse et likningssett \u003ca href=\"/no/encyclopedia/algebra/likninger-og-ulikheter/likninger/likningssett/hvordan-fremstille-likningssett-grafisk\"\u003egrafisk\u003c/a\u003e ved hjelp av en oppskrift som alltid vil ta deg i mål! \u003c/p\u003e      \u003cdiv class=\"tcolorbox foorule\" id=\"tcolobox-546\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Regel\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003ch3 class=\"rule-container-title\"\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eOppskrift\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003efor\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003egrafisk\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eløsning\u003c/span\u003e \u003c/h3\u003e \u003c/p\u003e\u003cp class=\"noindent\" \u003e      \u003c/p\u003e\u003cdl class=\"enumerate-enumitem\"\u003e\u003cdt class=\"enumerate-enumitem\"\u003e    1.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003eLøs begge likningene for \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ey\u003c/mi\u003e\u003c/math\u003e.         Det vil si at du skal ha \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ey\u003c/mi\u003e\u003c/math\u003e       alene på venstre side i begge uttrykkene. Det ser slik ut: \u003ctable class=\"equation-star\"\u003e\u003ctr\u003e\u003ctd\u003e         \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" class=\"equation\"\u003e                                                   \u003cmi  \u003ey\u003c/mi\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmi  \u003ea\u003c/mi\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmi  \u003eb\u003c/mi\u003e\u003cmo  class=\"MathClass-punc\" type=\"punct\"\u003e.\u003c/mo\u003e \u003c/math\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/table\u003e       \u003c/dd\u003e\u003cdt class=\"enumerate-enumitem\"\u003e    2.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003e         Uttrykkene         dine         er         nå         lineære         funksjoner.         Tegn         dem         i         samme         koordinatsystem.         \u003c/dd\u003e\u003cdt class=\"enumerate-enumitem\"\u003e     3.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003e         Les         av         \u003ca href=\"/no/encyclopedia/funksjoner/funksjonsteori/grunnleggende-om-funksjoner/skjaeringspunkter\"\u003eskjæringspunktet\u003c/a\u003e,         et         tall         fra         \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/math\u003e-aksen         og         et         tall         fra         \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ey\u003c/mi\u003e\u003c/math\u003e-aksen.         \u003c/dd\u003e\u003c/dl\u003e                                                                                                                      \u003c/div\u003e  \u003c/div\u003e                                                                                                                           \u003cdiv class=\"tcolorbox fooqaexample\" id=\"tcolobox-547\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e \u003cp class=\"indent\" \u003e     Eksempel 1\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003cb\u003e\u003cspan  class=\"ec-lmbx-12x-x-144\"\u003eLøs likningssettet\u003c/span\u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align\"\u003e                                       \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmi  \u003ey\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003c/mtd\u003e                                 \u003cmtd  class=\"align-even\"\u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                                              \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003cmstyle     id=\"x1-41006r1\"  class=\"label\" \u003e\u003c/mstyle\u003e\u003cmstyle  class=\"maketag\"\u003e\u003cmtext  \u003e(1)\u003c/mtext\u003e\u003c/mstyle\u003e\u003cmspace width=\"0.33em\" class=\"nbsp\" /\u003e                                                 \u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle 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\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e \u003cp class=\"noindent\" \u003e\u003c/b\u003e\u003c/p\u003e                                                                                                                     \u003cdiv class=\"lowerbox\"\u003e                                                                                                                                                                                                                                           \u003cp class=\"noindent\" \u003e          \u003c/p\u003e\u003cdl class=\"enumerate-enumitem\"\u003e\u003cdt class=\"enumerate-enumitem\"\u003e      1.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003eFørst løser du (\u003ca  href=\"#\"\u003e1\u003c/a\u003e) med hensyn til \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ey\u003c/mi\u003e\u003c/math type=\"divide\"\u003e:          \u003ctable class=\"equation-star\"\u003e\u003ctr\u003e\u003ctd\u003e          \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" class=\"equation\"\u003e                                                   \u003cmi  \u003ey\u003c/mi\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmo  class=\"MathClass-punc\" type=\"punct\"\u003e.\u003c/mo\u003e \u003c/math\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/table\u003e          \u003cp class=\"noindent\" \u003eDeretter løser du (\u003ca  href=\"#\"\u003e2\u003c/a\u003e) med hensyntil \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ey\u003c/mi\u003e\u003c/math type=\"divide\"\u003e:          \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                     \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmn\u003e4\u003c/mn\u003e\u003cmi  \u003ey\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                    \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e0\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                   \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                    \u003cmtd  class=\"align-label\"\u003e                                     \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmn\u003e4\u003c/mn\u003e\u003cmi  \u003ey\u003c/mi\u003e\u003c/mtd\u003e                                           \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e\u003cmn\u003e4\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e0\u003c/mn\u003e\u003cmspace width=\"1em\" class=\"quad\"/\u003e\u003cmo  class=\"MathClass-rel\"\u003e|\u003c/mo\u003e \u003cmo  class=\"MathClass-punc\" type=\"divide\"\u003e:\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                    \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                    \u003cmtd  class=\"align-label\"\u003e                                     \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ey\u003c/mi\u003e\u003c/mtd\u003e                                             \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e5\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                            \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                    \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e          \u003c/dd\u003e\u003cdt class=\"enumerate-enumitem\"\u003e      2.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003eTegn grafene til uttrykkene for \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ey\u003c/mi\u003e\u003c/math\u003e          i forrige punkt:          \u003cdiv class=\"center\"  \u003e  \u003cp class=\"noindent\" \u003e  \u003c/p\u003e\u003cp class=\"noindent\" \u003e\u003cimg src=\"https://images.houseofmath.com/overleaf-assets/images/2likn2ukjente.svg\" alt=\"De to linjene beskrevet over i ett koordinatsystem. De skjærer i (1,4)\" width=\"451\" height=\"451\"\u003e\u003c/p\u003e\u003c/div\u003e          \u003c/dd\u003e\u003cdt class=\"enumerate-enumitem\"\u003e      3.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003eLes av skjæringspunktet \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003c/math\u003e          og \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ey\u003c/mi\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e.          Skriv svaret slik: \u003ctable class=\"equation-star\"\u003e\u003ctr\u003e\u003ctd\u003e          \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" class=\"equation\"\u003e                                             \u003cmstyle  class=\"text\"\u003e\u003cmtext  \u003eSVAR:\u003c/mtext\u003e\u003c/mstyle\u003e\u003cmo  class=\"MathClass-open\" stretchy=\"false\"\u003e(\u003c/mo\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003cmo  class=\"MathClass-punc\"\u003e,\u003c/mo\u003e\u003cmi  \u003ey\u003c/mi\u003e\u003cmo  class=\"MathClass-close\" stretchy=\"false\"\u003e)\u003c/mo\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmo  class=\"MathClass-open\" stretchy=\"false\"\u003e(\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003cmo  class=\"MathClass-punc\"\u003e,\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmo  class=\"MathClass-close\" stretchy=\"false\"\u003e)\u003c/mo\u003e \u003c/math\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/table\u003e          \u003c/dd\u003e\u003c/dl\u003e                                                                                                                       \u003c/div\u003e  \u003c/div\u003e  \u003c/div\u003e                                                                                                                      \u003cp class=\"indent\" \u003e     Husk at det finnes tre ulike varianter for en løsning. Det er varianter der grafene ikke skjærer hverandre, varianter der grafene skjærer hverandre, og varianter der grafene ligger oppå hverandre. \u003c/p\u003e\u003cp class=\"indent\" \u003e     Dersom du blir usikker på løsningene du finner ved regning, kan du alltid få en fin oversikt ved å tegne grafene til likningene. Jeg føler ofte at det hjelper å ha et bilde på hvordan det hele henger sammen. Med litt trening vil du oppleve at du kan lage en skisse av disse i hodet. 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