Stelsels substitutie

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Substitutie

  1. \(\left\{\begin{matrix}x-y=4\\3x+4y=-44\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}x-5y=-50\\-6x=6y+12\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}-x-3y=-14\\-6x-6y=-12\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}x-2y=-8\\4x-5y=-29\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}3x+3y=-48\\6x-y=-54\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-4x+2y=0\\6x=y+4\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-x+y=13\\6x=-4y+2\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-3x-3y=9\\x+4y=15\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}-4y=8-4x\\2x+y=1\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}5x+5y=5\\-3x=y-13\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}-y=39-5x\\3x-3y=21\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}3x+2y=14\\4x-y=15\end{matrix}\right.\)

Substitutie

Verbetersleutel

  1. \(\left\{\begin{matrix}x-y=4\\3x+4y=-44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=y+4\\ 3x+4y=-44\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=y+4\\ 3.\left(y+4\right)+4y=-44\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=y+4\\ 3y+12+4y=-44\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=y+4\\ 7y=-44-12=-56\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=y+4\\ y=\frac{-56}{7}=-8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=.(-8)+4=-4\\ y=-8\end{matrix}\right.\\ \qquad V=\{(-4,-8)\}\)
  2. \(\left\{\begin{matrix}x-5y=-50\\-6x=6y+12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x-5y=-50\\-6x-6y=12\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}x=5y-50\\ -6x-6y=12\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=5y-50\\ -6.\left(5y-50\right)-6y=12\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=5y-50\\ -30y+300-6y=12\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=5y-50\\ -36y=12-300=-288\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=5y-50\\ y=\frac{-288}{-36}=8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=5.(8)-50=-10\\ y=8\end{matrix}\right.\\ \qquad V=\{(-10,8)\}\)
  3. \(\left\{\begin{matrix}-x-3y=-14\\-6x-6y=-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3y+14=x\\-6x-6y=-12\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=-3y+14\\ -6.\left(-3y+14\right)-6y=-12\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=-3y+14\\ 18y-84-6y=-12\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=-3y+14\\ 12y=-12+84=72\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-3y+14\\ y=\frac{72}{12}=6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-3.(6)+14=-4\\ y=6\end{matrix}\right.\\ \qquad V=\{(-4,6)\}\)
  4. \(\left\{\begin{matrix}x-2y=-8\\4x-5y=-29\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=2y-8\\ 4x-5y=-29\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=2y-8\\ 4.\left(2y-8\right)-5y=-29\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=2y-8\\ 8y-32-5y=-29\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=2y-8\\ 3y=-29+32=3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=2y-8\\ y=\frac{3}{3}=1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=2.(1)-8=-6\\ y=1\end{matrix}\right.\\ \qquad V=\{(-6,1)\}\)
  5. \(\left\{\begin{matrix}3x+3y=-48\\6x-y=-54\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+3y=-48\\ 6x+54=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}3x+3\left(6x+54\right)=-48\\y=6x+54\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}3x+18x+162=-48\\y=6x+54\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}21x=-48-162=-210\\y=6x+54\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-210}{21} = -10 \\ y=6x+54\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -10 \\ y=6.(-10)+54=-6\end{matrix}\right.\\ \qquad V=\{(-10,-6)\}\)
  6. \(\left\{\begin{matrix}-4x+2y=0\\6x=y+4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+2y=0\\6x-y=4\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-4x+2y=0\\ 6x-4=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-4x+2\left(6x-4\right)=0\\y=6x-4\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-4x+12x-8=0\\y=6x-4\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}8x=0+8=8\\y=6x-4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{8}{8} = 1 \\ y=6x-4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 1 \\ y=6.(1)-4=2\end{matrix}\right.\\ \qquad V=\{(1,2)\}\)
  7. \(\left\{\begin{matrix}-x+y=13\\6x=-4y+2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-x+y=13\\6x+4y=2\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}y-13=x\\6x+4y=2\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=y-13\\ 6.\left(y-13\right)+4y=2\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=y-13\\ 6y-78+4y=2\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=y-13\\ 10y=2+78=80\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=y-13\\ y=\frac{80}{10}=8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=.(8)-13=-5\\ y=8\end{matrix}\right.\\ \qquad V=\{(-5,8)\}\)
  8. \(\left\{\begin{matrix}-3x-3y=9\\x+4y=15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x-3y=9\\ x=-4y+15\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-3\left(-4y+15\right)-3y=9\\x=-4y+15\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}12y-45-3y=9\\x=-4y+15\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}9y=9+45=54\\x=-4y+15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{54}{9} = 6 \\ x=-4y+15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 6 \\ x=-4.(6)+15=-9\end{matrix}\right.\\ \qquad V=\{(-9,6)\}\)
  9. \(\left\{\begin{matrix}-4y=8-4x\\2x+y=1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-4y=8\\2x+y=1\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}4x-4y=8\\ y=-2x+1\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}4x-4\left(-2x+1\right)=8\\y=-2x+1\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}4x+8x-4=8\\y=-2x+1\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}12x=8+4=12\\y=-2x+1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{12}{12} = 1 \\ y=-2x+1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 1 \\ y=-2.(1)+1=-1\end{matrix}\right.\\ \qquad V=\{(1,-1)\}\)
  10. \(\left\{\begin{matrix}5x+5y=5\\-3x=y-13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x+5y=5\\-3x-y=-13\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}5x+5y=5\\ -3x+13=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}5x+5\left(-3x+13\right)=5\\y=-3x+13\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}5x-15x+65=5\\y=-3x+13\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-10x=5-65=-60\\y=-3x+13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-60}{-10} = 6 \\ y=-3x+13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 6 \\ y=-3.(6)+13=-5\end{matrix}\right.\\ \qquad V=\{(6,-5)\}\)
  11. \(\left\{\begin{matrix}-y=39-5x\\3x-3y=21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-y=39\\3x-3y=21\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}5x-39=y\\3x-3y=21\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}y=5x-39\\ 3x-3\left(5x-39\right)=21\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}y=5x-39\\ 3x-15x+117=21\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}y=5x-39\\ -12x=21-117=-96\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=5x-39\\ x=\frac{-96}{-12}=8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=5.(8)-39=1\\ x=8\end{matrix}\right.\\ \qquad V=\{(8,1)\}\)
  12. \(\left\{\begin{matrix}3x+2y=14\\4x-y=15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+2y=14\\ 4x-15=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}3x+2\left(4x-15\right)=14\\y=4x-15\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}3x+8x-30=14\\y=4x-15\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}11x=14+30=44\\y=4x-15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{44}{11} = 4 \\ y=4x-15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 4 \\ y=4.(4)-15=1\end{matrix}\right.\\ \qquad V=\{(4,1)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2026-03-07 04:23:15