Stelsels substitutie

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Substitutie

  1. \(\left\{\begin{matrix}-6x+5y=39\\x=-6y-27\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}-2x-5y=4\\x=2y+16\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}3x+4y=-3\\-x+5y=20\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}6y=-21-x\\2x+2y=8\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}2x+5y=-1\\3x=-y-21\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}5x+2y=-21\\-x-3y=25\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}3x-6y=-81\\-4x+y=38\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-2y=-38+4x\\-x-3y=-32\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}6x+5y=-28\\-x=3y-4\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-4x-6y=52\\x-5y=0\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}y=6+3x\\4x+6y=-52\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-2x+5y=5\\-6x=y-33\end{matrix}\right.\)

Substitutie

Verbetersleutel

  1. \(\left\{\begin{matrix}-6x+5y=39\\x=-6y-27\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+5y=39\\x+6y=-27\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-6x+5y=39\\ x=-6y-27\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-6\left(-6y-27\right)+5y=39\\x=-6y-27\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}36y+162+5y=39\\x=-6y-27\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}41y=39-162=-123\\x=-6y-27\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-123}{41} = -3 \\ x=-6y-27\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -3 \\ x=-6.(-3)-27=-9\end{matrix}\right.\\ \qquad V=\{(-9,-3)\}\)
  2. \(\left\{\begin{matrix}-2x-5y=4\\x=2y+16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-5y=4\\x-2y=16\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-2x-5y=4\\ x=2y+16\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-2\left(2y+16\right)-5y=4\\x=2y+16\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-4y-32-5y=4\\x=2y+16\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-9y=4+32=36\\x=2y+16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{36}{-9} = -4 \\ x=2y+16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -4 \\ x=2.(-4)+16=8\end{matrix}\right.\\ \qquad V=\{(8,-4)\}\)
  3. \(\left\{\begin{matrix}3x+4y=-3\\-x+5y=20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+4y=-3\\ 5y-20=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}3\left(5y-20\right)+4y=-3\\x=5y-20\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}15y-60+4y=-3\\x=5y-20\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}19y=-3+60=57\\x=5y-20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{57}{19} = 3 \\ x=5y-20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 3 \\ x=5.(3)-20=-5\end{matrix}\right.\\ \qquad V=\{(-5,3)\}\)
  4. \(\left\{\begin{matrix}6y=-21-x\\2x+2y=8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x+6y=-21\\2x+2y=8\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}x=-6y-21\\ 2x+2y=8\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=-6y-21\\ 2.\left(-6y-21\right)+2y=8\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=-6y-21\\ -12y-42+2y=8\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=-6y-21\\ -10y=8+42=50\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-6y-21\\ y=\frac{50}{-10}=-5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-6.(-5)-21=9\\ y=-5\end{matrix}\right.\\ \qquad V=\{(9,-5)\}\)
  5. \(\left\{\begin{matrix}2x+5y=-1\\3x=-y-21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+5y=-1\\3x+y=-21\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}2x+5y=-1\\ y=-3x-21\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}2x+5\left(-3x-21\right)=-1\\y=-3x-21\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}2x-15x-105=-1\\y=-3x-21\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-13x=-1+105=104\\y=-3x-21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{104}{-13} = -8 \\ y=-3x-21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -8 \\ y=-3.(-8)-21=3\end{matrix}\right.\\ \qquad V=\{(-8,3)\}\)
  6. \(\left\{\begin{matrix}5x+2y=-21\\-x-3y=25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x+2y=-21\\ -3y-25=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}5\left(-3y-25\right)+2y=-21\\x=-3y-25\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-15y-125+2y=-21\\x=-3y-25\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-13y=-21+125=104\\x=-3y-25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{104}{-13} = -8 \\ x=-3y-25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -8 \\ x=-3.(-8)-25=-1\end{matrix}\right.\\ \qquad V=\{(-1,-8)\}\)
  7. \(\left\{\begin{matrix}3x-6y=-81\\-4x+y=38\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-6y=-81\\ y=4x+38\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}3x-6\left(4x+38\right)=-81\\y=4x+38\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}3x-24x-228=-81\\y=4x+38\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-21x=-81+228=147\\y=4x+38\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{147}{-21} = -7 \\ y=4x+38\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -7 \\ y=4.(-7)+38=10\end{matrix}\right.\\ \qquad V=\{(-7,10)\}\)
  8. \(\left\{\begin{matrix}-2y=-38+4x\\-x-3y=-32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-2y=-38\\-x-3y=-32\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-4x-2y=-38\\ -3y+32=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-4\left(-3y+32\right)-2y=-38\\x=-3y+32\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}12y-128-2y=-38\\x=-3y+32\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}10y=-38+128=90\\x=-3y+32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{90}{10} = 9 \\ x=-3y+32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 9 \\ x=-3.(9)+32=5\end{matrix}\right.\\ \qquad V=\{(5,9)\}\)
  9. \(\left\{\begin{matrix}6x+5y=-28\\-x=3y-4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+5y=-28\\-x-3y=-4\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}6x+5y=-28\\ -3y+4=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}6\left(-3y+4\right)+5y=-28\\x=-3y+4\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-18y+24+5y=-28\\x=-3y+4\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-13y=-28-24=-52\\x=-3y+4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-52}{-13} = 4 \\ x=-3y+4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 4 \\ x=-3.(4)+4=-8\end{matrix}\right.\\ \qquad V=\{(-8,4)\}\)
  10. \(\left\{\begin{matrix}-4x-6y=52\\x-5y=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-6y=52\\ x=5y+0\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-4\left(5y+0\right)-6y=52\\x=5y+0\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-20y+0-6y=52\\x=5y+0\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-26y=52+0=52\\x=5y+0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{52}{-26} = -2 \\ x=5y+0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -2 \\ x=5.(-2)+0=-10\end{matrix}\right.\\ \qquad V=\{(-10,-2)\}\)
  11. \(\left\{\begin{matrix}y=6+3x\\4x+6y=-52\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+y=6\\4x+6y=-52\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}y=3x+6\\ 4x+6y=-52\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}y=3x+6\\ 4x+6\left(3x+6\right)=-52\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}y=3x+6\\ 4x+18x+36=-52\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}y=3x+6\\ 22x=-52-36=-88\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=3x+6\\ x=\frac{-88}{22}=-4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=3.(-4)+6=-6\\ x=-4\end{matrix}\right.\\ \qquad V=\{(-4,-6)\}\)
  12. \(\left\{\begin{matrix}-2x+5y=5\\-6x=y-33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+5y=5\\-6x-y=-33\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-2x+5y=5\\ -6x+33=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-2x+5\left(-6x+33\right)=5\\y=-6x+33\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-2x-30x+165=5\\y=-6x+33\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-32x=5-165=-160\\y=-6x+33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-160}{-32} = 5 \\ y=-6x+33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 5 \\ y=-6.(5)+33=3\end{matrix}\right.\\ \qquad V=\{(5,3)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-13 22:57:23