Stelsels substitutie

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Substitutie

  1. \(\left\{\begin{matrix}-5y=-59+6x\\3x-y=5\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}-5y=-19+4x\\-3x-y=5\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}5x-6y=100\\x=2y+28\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-2x-5y=16\\x+6y=-29\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-3x+5y=-55\\3x-y=23\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-x+4y=-30\\-4x=2y-12\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-3x-5y=-35\\x-6y=4\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-6x+2y=-54\\-x=3y+1\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}-5y=34-4x\\x+3y=0\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}x-2y=7\\-5x+4y=-41\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}3x+5y=-2\\-x-4y=-11\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}2y=27-x\\4x-3y=-2\end{matrix}\right.\)

Substitutie

Verbetersleutel

  1. \(\left\{\begin{matrix}-5y=-59+6x\\3x-y=5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x-5y=-59\\3x-y=5\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-6x-5y=-59\\ 3x-5=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-6x-5\left(3x-5\right)=-59\\y=3x-5\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-6x-15x+25=-59\\y=3x-5\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-21x=-59-25=-84\\y=3x-5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-84}{-21} = 4 \\ y=3x-5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 4 \\ y=3.(4)-5=7\end{matrix}\right.\\ \qquad V=\{(4,7)\}\)
  2. \(\left\{\begin{matrix}-5y=-19+4x\\-3x-y=5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-5y=-19\\-3x-y=5\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-4x-5y=-19\\ -3x-5=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-4x-5\left(-3x-5\right)=-19\\y=-3x-5\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-4x+15x+25=-19\\y=-3x-5\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}11x=-19-25=-44\\y=-3x-5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-44}{11} = -4 \\ y=-3x-5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -4 \\ y=-3.(-4)-5=7\end{matrix}\right.\\ \qquad V=\{(-4,7)\}\)
  3. \(\left\{\begin{matrix}5x-6y=100\\x=2y+28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-6y=100\\x-2y=28\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}5x-6y=100\\ x=2y+28\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}5\left(2y+28\right)-6y=100\\x=2y+28\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}10y+140-6y=100\\x=2y+28\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}4y=100-140=-40\\x=2y+28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-40}{4} = -10 \\ x=2y+28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -10 \\ x=2.(-10)+28=8\end{matrix}\right.\\ \qquad V=\{(8,-10)\}\)
  4. \(\left\{\begin{matrix}-2x-5y=16\\x+6y=-29\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-5y=16\\ x=-6y-29\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-2\left(-6y-29\right)-5y=16\\x=-6y-29\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}12y+58-5y=16\\x=-6y-29\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}7y=16-58=-42\\x=-6y-29\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-42}{7} = -6 \\ x=-6y-29\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -6 \\ x=-6.(-6)-29=7\end{matrix}\right.\\ \qquad V=\{(7,-6)\}\)
  5. \(\left\{\begin{matrix}-3x+5y=-55\\3x-y=23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+5y=-55\\ 3x-23=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-3x+5\left(3x-23\right)=-55\\y=3x-23\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-3x+15x-115=-55\\y=3x-23\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}12x=-55+115=60\\y=3x-23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{60}{12} = 5 \\ y=3x-23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 5 \\ y=3.(5)-23=-8\end{matrix}\right.\\ \qquad V=\{(5,-8)\}\)
  6. \(\left\{\begin{matrix}-x+4y=-30\\-4x=2y-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-x+4y=-30\\-4x-2y=-12\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}4y+30=x\\-4x-2y=-12\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=4y+30\\ -4.\left(4y+30\right)-2y=-12\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=4y+30\\ -16y-120-2y=-12\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=4y+30\\ -18y=-12+120=108\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=4y+30\\ y=\frac{108}{-18}=-6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=4.(-6)+30=6\\ y=-6\end{matrix}\right.\\ \qquad V=\{(6,-6)\}\)
  7. \(\left\{\begin{matrix}-3x-5y=-35\\x-6y=4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x-5y=-35\\ x=6y+4\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-3\left(6y+4\right)-5y=-35\\x=6y+4\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-18y-12-5y=-35\\x=6y+4\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-23y=-35+12=-23\\x=6y+4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-23}{-23} = 1 \\ x=6y+4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 1 \\ x=6.(1)+4=10\end{matrix}\right.\\ \qquad V=\{(10,1)\}\)
  8. \(\left\{\begin{matrix}-6x+2y=-54\\-x=3y+1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+2y=-54\\-x-3y=1\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-6x+2y=-54\\ -3y-1=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-6\left(-3y-1\right)+2y=-54\\x=-3y-1\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}18y+6+2y=-54\\x=-3y-1\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}20y=-54-6=-60\\x=-3y-1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-60}{20} = -3 \\ x=-3y-1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -3 \\ x=-3.(-3)-1=8\end{matrix}\right.\\ \qquad V=\{(8,-3)\}\)
  9. \(\left\{\begin{matrix}-5y=34-4x\\x+3y=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-5y=34\\x+3y=0\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}4x-5y=34\\ x=-3y+0\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}4\left(-3y+0\right)-5y=34\\x=-3y+0\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-12y+0-5y=34\\x=-3y+0\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-17y=34+0=34\\x=-3y+0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{34}{-17} = -2 \\ x=-3y+0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -2 \\ x=-3.(-2)+0=6\end{matrix}\right.\\ \qquad V=\{(6,-2)\}\)
  10. \(\left\{\begin{matrix}x-2y=7\\-5x+4y=-41\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=2y+7\\ -5x+4y=-41\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=2y+7\\ -5.\left(2y+7\right)+4y=-41\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=2y+7\\ -10y-35+4y=-41\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=2y+7\\ -6y=-41+35=-6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=2y+7\\ y=\frac{-6}{-6}=1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=2.(1)+7=9\\ y=1\end{matrix}\right.\\ \qquad V=\{(9,1)\}\)
  11. \(\left\{\begin{matrix}3x+5y=-2\\-x-4y=-11\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+5y=-2\\ -4y+11=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}3\left(-4y+11\right)+5y=-2\\x=-4y+11\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-12y+33+5y=-2\\x=-4y+11\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-7y=-2-33=-35\\x=-4y+11\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-35}{-7} = 5 \\ x=-4y+11\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 5 \\ x=-4.(5)+11=-9\end{matrix}\right.\\ \qquad V=\{(-9,5)\}\)
  12. \(\left\{\begin{matrix}2y=27-x\\4x-3y=-2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x+2y=27\\4x-3y=-2\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}x=-2y+27\\ 4x-3y=-2\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=-2y+27\\ 4.\left(-2y+27\right)-3y=-2\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=-2y+27\\ -8y+108-3y=-2\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=-2y+27\\ -11y=-2-108=-110\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-2y+27\\ y=\frac{-110}{-11}=10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-2.(10)+27=7\\ y=10\end{matrix}\right.\\ \qquad V=\{(7,10)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2026-08-14 21:14:29