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Liceul Teoretic “ Petru Cercel ” Targoviste

Liceul Teoretic “ Petru Cercel ” Targoviste. Sisteme de ecuatii liniare. Coordonator : Nica Ionut. Elev : Ciubotariu Ionut. Sisteme de 2 ecuatii cu 2 necunoscute. Def : un sistem liniar de doua ecuatii cu doua necunoscute are forma : a1x+b1y+c1 =d1 a2y+b2y+c2 =d2

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Liceul Teoretic “ Petru Cercel ” Targoviste

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  1. LiceulTeoretic “PetruCercel” Targoviste Sisteme de ecuatiiliniare Coordonator: NicaIonut Elev: CiubotariuIonut

  2. Sisteme de 2 ecuatii cu 2 necunoscute Def: un sistemliniar de douaecuatiicudouanecunoscute are forma : a1x+b1y+c1 =d1 a2y+b2y+c2 =d2 undea,b,c,dapartin la R.

  3. Metode de rezolvare 1.Metoda combinatiilor liniare 2.Metoda substitutiei 3.Metoda eliminarii (Gauss) 4.Regula lui Cramer

  4. Sisteme de 3 ecuatii cu 3 necunoscute Def:Unsistemliniar de treiecuatiicutreinecunoscute are forma : a1x+b1y+c1=d1 a2y+b2y+c2=d2 a3y+b3y+c3=d3 Undea,b,c,dapartin la R.

  5. Metode de rezolvare 1.Metoda combinatiilor liniare 2.Metoda eliminarii (Gauss) 3.Regula lui Cramer 4. Metoda matricii inverse

  6. Sisteme de n ecuatii cu m necunoscute Def:Unsistemliniar cu n ecuatii cu m necunoscute are forma: a11x1+a12x2+…+a1nxn=b1 a21x1+a22x2+ …+a2nxn=b2 …………………………. Am1x1+am2x2+…+amnxn=bm

  7. Ecuatii Chimice • In procesul de fotosintezaplanteleutilizeazaenergia radiate de soarepentru a transformadioxidul de carbon (CO2)siapa(H2O)in glucoza(C6H12O6)sioxigen(O2) • Ecuatiachimica a reactieieste de forma: x1CO2+x2H2O →x3O2+x4C6H12O6. Pentru a obtineechilibrul(balanta)ecuatieitrebuiesaalegem x1,x2,x3,x4astfelincatnumarul de atomi de carbon hidrogensioxigen din ceidoimembrisa fie acelasi.Deoarecedioxidul de carbon contine un atom de carbon,iarglucozacontinesase,atuncipentruegalizareanumarului de atomi de carbon trebuiesaavem x1=6x4.

  8. Analog,pentruatomii de oxigensi respective hidrogenavemecuatiile: 2x1+x2=2x3+6x4,2x2=12x4.Cele tri ecuatiiconduc la sistemul: Solutia sistemuluieste :x1=6 גּ X2= 6 גּ X3=6 גּ X4= גּ גּ ≥0 ; Pentruגּ =1 se obtine Solutia particulara x1=x2=x3=6,x4=1 siecuatia are forma: 6CO2+6H2O→6O2+C­6H12O6­.

  9. Cuprins Sisteme de 2 ecuatii cu 2 necunoscute-definitie ……………………………slide 2 Sisteme de 2 ecuatii cu 2 necunoscute-metode de rezolvare…………….slide 3 Sisteme de 3 ecuatii cu 3 necunoscute-definite ……………………………slide 4 Sisteme de 3 ecuatii cu 3 necunoscute-metode de rezolvare ……………slide 5 Sisteme de n ecuatii cu m necunoscute……………………………………..slide 6 Ecuatichimice…………………………………………………………………….slide 7

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