Stelsels substitutie

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Substitutie

  1. \(\left\{\begin{matrix}-2x-3y=26\\x=-5y-34\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}-3x-y=-5\\6x+4y=14\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}4x-5y=-9\\-x=6y-63\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-4x-6y=50\\x=-3y-26\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}5y=-82-4x\\-x+6y=-52\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}3x+6y=-21\\-x=5y+4\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}5x-2y=15\\-3x=y+13\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}3x+y=14\\4x=5y-32\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}6x+y=-35\\-3x-6y=-21\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-x-3y=-17\\-5x=4y-52\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}-2x+6y=-80\\2x+y=10\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-3x+3y=-6\\-4x=y-23\end{matrix}\right.\)

Substitutie

Verbetersleutel

  1. \(\left\{\begin{matrix}-2x-3y=26\\x=-5y-34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-3y=26\\x+5y=-34\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-2x-3y=26\\ x=-5y-34\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-2\left(-5y-34\right)-3y=26\\x=-5y-34\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}10y+68-3y=26\\x=-5y-34\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}7y=26-68=-42\\x=-5y-34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-42}{7} = -6 \\ x=-5y-34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -6 \\ x=-5.(-6)-34=-4\end{matrix}\right.\\ \qquad V=\{(-4,-6)\}\)
  2. \(\left\{\begin{matrix}-3x-y=-5\\6x+4y=14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+5=y\\6x+4y=14\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}y=-3x+5\\ 6x+4\left(-3x+5\right)=14\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}y=-3x+5\\ 6x-12x+20=14\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}y=-3x+5\\ -6x=14-20=-6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-3x+5\\ x=\frac{-6}{-6}=1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-3.(1)+5=2\\ x=1\end{matrix}\right.\\ \qquad V=\{(1,2)\}\)
  3. \(\left\{\begin{matrix}4x-5y=-9\\-x=6y-63\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-5y=-9\\-x-6y=-63\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}4x-5y=-9\\ -6y+63=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}4\left(-6y+63\right)-5y=-9\\x=-6y+63\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-24y+252-5y=-9\\x=-6y+63\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-29y=-9-252=-261\\x=-6y+63\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-261}{-29} = 9 \\ x=-6y+63\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 9 \\ x=-6.(9)+63=9\end{matrix}\right.\\ \qquad V=\{(9,9)\}\)
  4. \(\left\{\begin{matrix}-4x-6y=50\\x=-3y-26\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-6y=50\\x+3y=-26\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-4x-6y=50\\ x=-3y-26\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-4\left(-3y-26\right)-6y=50\\x=-3y-26\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}12y+104-6y=50\\x=-3y-26\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}6y=50-104=-54\\x=-3y-26\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-54}{6} = -9 \\ x=-3y-26\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -9 \\ x=-3.(-9)-26=1\end{matrix}\right.\\ \qquad V=\{(1,-9)\}\)
  5. \(\left\{\begin{matrix}5y=-82-4x\\-x+6y=-52\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+5y=-82\\-x+6y=-52\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}4x+5y=-82\\ 6y+52=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}4\left(6y+52\right)+5y=-82\\x=6y+52\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}24y+208+5y=-82\\x=6y+52\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}29y=-82-208=-290\\x=6y+52\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-290}{29} = -10 \\ x=6y+52\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -10 \\ x=6.(-10)+52=-8\end{matrix}\right.\\ \qquad V=\{(-8,-10)\}\)
  6. \(\left\{\begin{matrix}3x+6y=-21\\-x=5y+4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+6y=-21\\-x-5y=4\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}3x+6y=-21\\ -5y-4=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}3\left(-5y-4\right)+6y=-21\\x=-5y-4\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-15y-12+6y=-21\\x=-5y-4\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-9y=-21+12=-9\\x=-5y-4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-9}{-9} = 1 \\ x=-5y-4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 1 \\ x=-5.(1)-4=-9\end{matrix}\right.\\ \qquad V=\{(-9,1)\}\)
  7. \(\left\{\begin{matrix}5x-2y=15\\-3x=y+13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-2y=15\\-3x-y=13\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}5x-2y=15\\ -3x-13=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}5x-2\left(-3x-13\right)=15\\y=-3x-13\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}5x+6x+26=15\\y=-3x-13\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}11x=15-26=-11\\y=-3x-13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-11}{11} = -1 \\ y=-3x-13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -1 \\ y=-3.(-1)-13=-10\end{matrix}\right.\\ \qquad V=\{(-1,-10)\}\)
  8. \(\left\{\begin{matrix}3x+y=14\\4x=5y-32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+y=14\\4x-5y=-32\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}y=-3x+14\\ 4x-5y=-32\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}y=-3x+14\\ 4x-5\left(-3x+14\right)=-32\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}y=-3x+14\\ 4x+15x-70=-32\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}y=-3x+14\\ 19x=-32+70=38\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-3x+14\\ x=\frac{38}{19}=2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-3.(2)+14=8\\ x=2\end{matrix}\right.\\ \qquad V=\{(2,8)\}\)
  9. \(\left\{\begin{matrix}6x+y=-35\\-3x-6y=-21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-6x-35\\ -3x-6y=-21\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}y=-6x-35\\ -3x-6\left(-6x-35\right)=-21\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}y=-6x-35\\ -3x+36x+210=-21\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}y=-6x-35\\ 33x=-21-210=-231\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-6x-35\\ x=\frac{-231}{33}=-7\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-6.(-7)-35=7\\ x=-7\end{matrix}\right.\\ \qquad V=\{(-7,7)\}\)
  10. \(\left\{\begin{matrix}-x-3y=-17\\-5x=4y-52\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-x-3y=-17\\-5x-4y=-52\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-3y+17=x\\-5x-4y=-52\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=-3y+17\\ -5.\left(-3y+17\right)-4y=-52\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=-3y+17\\ 15y-85-4y=-52\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=-3y+17\\ 11y=-52+85=33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-3y+17\\ y=\frac{33}{11}=3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-3.(3)+17=8\\ y=3\end{matrix}\right.\\ \qquad V=\{(8,3)\}\)
  11. \(\left\{\begin{matrix}-2x+6y=-80\\2x+y=10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+6y=-80\\ y=-2x+10\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-2x+6\left(-2x+10\right)=-80\\y=-2x+10\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-2x-12x+60=-80\\y=-2x+10\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-14x=-80-60=-140\\y=-2x+10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-140}{-14} = 10 \\ y=-2x+10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 10 \\ y=-2.(10)+10=-10\end{matrix}\right.\\ \qquad V=\{(10,-10)\}\)
  12. \(\left\{\begin{matrix}-3x+3y=-6\\-4x=y-23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+3y=-6\\-4x-y=-23\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-3x+3y=-6\\ -4x+23=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-3x+3\left(-4x+23\right)=-6\\y=-4x+23\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-3x-12x+69=-6\\y=-4x+23\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-15x=-6-69=-75\\y=-4x+23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-75}{-15} = 5 \\ y=-4x+23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 5 \\ y=-4.(5)+23=3\end{matrix}\right.\\ \qquad V=\{(5,3)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-07 07:24:33