Likningssystem (grafisk løsning)

Et likningssystem er rett og slett en samling likninger. Frem til nå har du jobbet med én likning med én ukjent (en variabel). Nå skal du lære to likninger med to ukjente (to variabler). Du skal lære tre metoder for å løse likningssystemer: Grafisk løsning, innsettingsmetoden og addisjonsmetoden. Vi begynner med grafisk løsning.

Grafisk løsning

Regel

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)Først løser du (1) med hensyn på y : y = 2 x + 2 . Deretter løser du (2) med hensyn på y : \begin{array}{l} 4 y + 4 x & = 20 \\ 4 y & = - 4 x + 20 | : 4 \\ y & = - x + 5 \end{array} Du kan nå plotte linjene y = 2 x + 2 og y = - x + 5 : Les av skjæringspunktet x = 1 og y = 4 .  SVAR: (x, y) = (1, 4)Vil du vite mer? Registrer deg Det er gratis!Forrige oppslag Aktiviteter 8 Neste oppslag Likningssystem (innsetting)Hjem 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":{"h1":"Likningssystem (grafisk løsning)","metaDescription":"Et likningssystem er en samling av likninger. 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