Stelsels substitutie

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Substitutie

  1. \(\left\{\begin{matrix}5y=-37+3x\\2x+y=3\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}6x+5y=71\\-x-2y=-20\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}-x-3y=-6\\-6x=6y-48\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-x+y=13\\3x+4y=24\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}5y=-36+x\\-5x-3y=16\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-4x+2y=52\\x=-5y+20\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-2y=64+6x\\x+4y=-18\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-y=-2+2x\\3x-3y=-15\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}-6y=-57-x\\5x-5y=-60\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}4x+6y=-74\\2x-y=-9\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}2x+y=17\\6x=5y+27\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-6x+3y=-9\\x=4y+5\end{matrix}\right.\)

Substitutie

Verbetersleutel

  1. \(\left\{\begin{matrix}5y=-37+3x\\2x+y=3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+5y=-37\\2x+y=3\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-3x+5y=-37\\ y=-2x+3\end{matrix}\right.\text{(Afzonderen onbekende met coƫff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-3x+5\left(-2x+3\right)=-37\\y=-2x+3\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-3x-10x+15=-37\\y=-2x+3\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-13x=-37-15=-52\\y=-2x+3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-52}{-13} = 4 \\ y=-2x+3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 4 \\ y=-2.(4)+3=-5\end{matrix}\right.\\ \qquad V=\{(4,-5)\}\)
  2. \(\left\{\begin{matrix}6x+5y=71\\-x-2y=-20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+5y=71\\ -2y+20=x\end{matrix}\right.\text{(Afzonderen onbekende met coƫff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}6\left(-2y+20\right)+5y=71\\x=-2y+20\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-12y+120+5y=71\\x=-2y+20\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-7y=71-120=-49\\x=-2y+20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-49}{-7} = 7 \\ x=-2y+20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 7 \\ x=-2.(7)+20=6\end{matrix}\right.\\ \qquad V=\{(6,7)\}\)
  3. \(\left\{\begin{matrix}-x-3y=-6\\-6x=6y-48\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-x-3y=-6\\-6x-6y=-48\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-3y+6=x\\-6x-6y=-48\end{matrix}\right.\text{(Afzonderen onbekende met coƫff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=-3y+6\\ -6.\left(-3y+6\right)-6y=-48\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=-3y+6\\ 18y-36-6y=-48\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=-3y+6\\ 12y=-48+36=-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-3y+6\\ y=\frac{-12}{12}=-1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-3.(-1)+6=9\\ y=-1\end{matrix}\right.\\ \qquad V=\{(9,-1)\}\)
  4. \(\left\{\begin{matrix}-x+y=13\\3x+4y=24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y-13=x\\3x+4y=24\end{matrix}\right.\text{(Afzonderen onbekende met coƫff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=y-13\\ 3.\left(y-13\right)+4y=24\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=y-13\\ 3y-39+4y=24\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=y-13\\ 7y=24+39=63\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=y-13\\ y=\frac{63}{7}=9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=.(9)-13=-4\\ y=9\end{matrix}\right.\\ \qquad V=\{(-4,9)\}\)
  5. \(\left\{\begin{matrix}5y=-36+x\\-5x-3y=16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-x+5y=-36\\-5x-3y=16\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}5y+36=x\\-5x-3y=16\end{matrix}\right.\text{(Afzonderen onbekende met coƫff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=5y+36\\ -5.\left(5y+36\right)-3y=16\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=5y+36\\ -25y-180-3y=16\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=5y+36\\ -28y=16+180=196\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=5y+36\\ y=\frac{196}{-28}=-7\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=5.(-7)+36=1\\ y=-7\end{matrix}\right.\\ \qquad V=\{(1,-7)\}\)
  6. \(\left\{\begin{matrix}-4x+2y=52\\x=-5y+20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+2y=52\\x+5y=20\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-4x+2y=52\\ x=-5y+20\end{matrix}\right.\text{(Afzonderen onbekende met coƫff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-4\left(-5y+20\right)+2y=52\\x=-5y+20\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}20y-80+2y=52\\x=-5y+20\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}22y=52+80=132\\x=-5y+20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{132}{22} = 6 \\ x=-5y+20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 6 \\ x=-5.(6)+20=-10\end{matrix}\right.\\ \qquad V=\{(-10,6)\}\)
  7. \(\left\{\begin{matrix}-2y=64+6x\\x+4y=-18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x-2y=64\\x+4y=-18\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-6x-2y=64\\ x=-4y-18\end{matrix}\right.\text{(Afzonderen onbekende met coƫff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-6\left(-4y-18\right)-2y=64\\x=-4y-18\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}24y+108-2y=64\\x=-4y-18\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}22y=64-108=-44\\x=-4y-18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-44}{22} = -2 \\ x=-4y-18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -2 \\ x=-4.(-2)-18=-10\end{matrix}\right.\\ \qquad V=\{(-10,-2)\}\)
  8. \(\left\{\begin{matrix}-y=-2+2x\\3x-3y=-15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-y=-2\\3x-3y=-15\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-2x+2=y\\3x-3y=-15\end{matrix}\right.\text{(Afzonderen onbekende met coƫff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}y=-2x+2\\ 3x-3\left(-2x+2\right)=-15\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}y=-2x+2\\ 3x+6x-6=-15\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}y=-2x+2\\ 9x=-15+6=-9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-2x+2\\ x=\frac{-9}{9}=-1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-2.(-1)+2=4\\ x=-1\end{matrix}\right.\\ \qquad V=\{(-1,4)\}\)
  9. \(\left\{\begin{matrix}-6y=-57-x\\5x-5y=-60\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x-6y=-57\\5x-5y=-60\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}x=6y-57\\ 5x-5y=-60\end{matrix}\right.\text{(Afzonderen onbekende met coƫff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=6y-57\\ 5.\left(6y-57\right)-5y=-60\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=6y-57\\ 30y-285-5y=-60\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=6y-57\\ 25y=-60+285=225\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=6y-57\\ y=\frac{225}{25}=9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=6.(9)-57=-3\\ y=9\end{matrix}\right.\\ \qquad V=\{(-3,9)\}\)
  10. \(\left\{\begin{matrix}4x+6y=-74\\2x-y=-9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+6y=-74\\ 2x+9=y\end{matrix}\right.\text{(Afzonderen onbekende met coƫff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}4x+6\left(2x+9\right)=-74\\y=2x+9\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}4x+12x+54=-74\\y=2x+9\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}16x=-74-54=-128\\y=2x+9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-128}{16} = -8 \\ y=2x+9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -8 \\ y=2.(-8)+9=-7\end{matrix}\right.\\ \qquad V=\{(-8,-7)\}\)
  11. \(\left\{\begin{matrix}2x+y=17\\6x=5y+27\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+y=17\\6x-5y=27\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}y=-2x+17\\ 6x-5y=27\end{matrix}\right.\text{(Afzonderen onbekende met coƫff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}y=-2x+17\\ 6x-5\left(-2x+17\right)=27\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}y=-2x+17\\ 6x+10x-85=27\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}y=-2x+17\\ 16x=27+85=112\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-2x+17\\ x=\frac{112}{16}=7\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-2.(7)+17=3\\ x=7\end{matrix}\right.\\ \qquad V=\{(7,3)\}\)
  12. \(\left\{\begin{matrix}-6x+3y=-9\\x=4y+5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+3y=-9\\x-4y=5\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-6x+3y=-9\\ x=4y+5\end{matrix}\right.\text{(Afzonderen onbekende met coƫff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-6\left(4y+5\right)+3y=-9\\x=4y+5\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-24y-30+3y=-9\\x=4y+5\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-21y=-9+30=21\\x=4y+5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{21}{-21} = -1 \\ x=4y+5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -1 \\ x=4.(-1)+5=1\end{matrix}\right.\\ \qquad V=\{(1,-1)\}\)
Oefeningengenerator wiskundeoefeningen.be 2025-05-11 08:59:52
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