Stelsels substitutie

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Substitutie

  1. \(\left\{\begin{matrix}4x-5y=-54\\-x=2y-19\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}5x-4y=67\\x=-2y-9\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}6x+3y=-57\\x-5y=18\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}3x+3y=-51\\x-5y=37\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-5x-y=34\\3x+2y=-12\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}2x+3y=11\\2x=y+23\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-4y=4+3x\\x-6y=28\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}5x+5y=-5\\x-4y=-36\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}x-4y=39\\4x-5y=68\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}5y=-10+5x\\x+6y=-61\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}5x-6y=-7\\x=-3y-14\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}3x-5y=6\\4x-y=-9\end{matrix}\right.\)

Substitutie

Verbetersleutel

  1. \(\left\{\begin{matrix}4x-5y=-54\\-x=2y-19\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-5y=-54\\-x-2y=-19\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}4x-5y=-54\\ -2y+19=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}4\left(-2y+19\right)-5y=-54\\x=-2y+19\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-8y+76-5y=-54\\x=-2y+19\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-13y=-54-76=-130\\x=-2y+19\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-130}{-13} = 10 \\ x=-2y+19\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 10 \\ x=-2.(10)+19=-1\end{matrix}\right.\\ \qquad V=\{(-1,10)\}\)
  2. \(\left\{\begin{matrix}5x-4y=67\\x=-2y-9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-4y=67\\x+2y=-9\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}5x-4y=67\\ x=-2y-9\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}5\left(-2y-9\right)-4y=67\\x=-2y-9\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-10y-45-4y=67\\x=-2y-9\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-14y=67+45=112\\x=-2y-9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{112}{-14} = -8 \\ x=-2y-9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -8 \\ x=-2.(-8)-9=7\end{matrix}\right.\\ \qquad V=\{(7,-8)\}\)
  3. \(\left\{\begin{matrix}6x+3y=-57\\x-5y=18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+3y=-57\\ x=5y+18\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}6\left(5y+18\right)+3y=-57\\x=5y+18\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}30y+108+3y=-57\\x=5y+18\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}33y=-57-108=-165\\x=5y+18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-165}{33} = -5 \\ x=5y+18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -5 \\ x=5.(-5)+18=-7\end{matrix}\right.\\ \qquad V=\{(-7,-5)\}\)
  4. \(\left\{\begin{matrix}3x+3y=-51\\x-5y=37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+3y=-51\\ x=5y+37\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}3\left(5y+37\right)+3y=-51\\x=5y+37\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}15y+111+3y=-51\\x=5y+37\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}18y=-51-111=-162\\x=5y+37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-162}{18} = -9 \\ x=5y+37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -9 \\ x=5.(-9)+37=-8\end{matrix}\right.\\ \qquad V=\{(-8,-9)\}\)
  5. \(\left\{\begin{matrix}-5x-y=34\\3x+2y=-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-34=y\\3x+2y=-12\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}y=-5x-34\\ 3x+2\left(-5x-34\right)=-12\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}y=-5x-34\\ 3x-10x-68=-12\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}y=-5x-34\\ -7x=-12+68=56\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-5x-34\\ x=\frac{56}{-7}=-8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-5.(-8)-34=6\\ x=-8\end{matrix}\right.\\ \qquad V=\{(-8,6)\}\)
  6. \(\left\{\begin{matrix}2x+3y=11\\2x=y+23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+3y=11\\2x-y=23\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}2x+3y=11\\ 2x-23=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}2x+3\left(2x-23\right)=11\\y=2x-23\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}2x+6x-69=11\\y=2x-23\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}8x=11+69=80\\y=2x-23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{80}{8} = 10 \\ y=2x-23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 10 \\ y=2.(10)-23=-3\end{matrix}\right.\\ \qquad V=\{(10,-3)\}\)
  7. \(\left\{\begin{matrix}-4y=4+3x\\x-6y=28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x-4y=4\\x-6y=28\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-3x-4y=4\\ x=6y+28\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-3\left(6y+28\right)-4y=4\\x=6y+28\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-18y-84-4y=4\\x=6y+28\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-22y=4+84=88\\x=6y+28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{88}{-22} = -4 \\ x=6y+28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -4 \\ x=6.(-4)+28=4\end{matrix}\right.\\ \qquad V=\{(4,-4)\}\)
  8. \(\left\{\begin{matrix}5x+5y=-5\\x-4y=-36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x+5y=-5\\ x=4y-36\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}5\left(4y-36\right)+5y=-5\\x=4y-36\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}20y-180+5y=-5\\x=4y-36\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}25y=-5+180=175\\x=4y-36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{175}{25} = 7 \\ x=4y-36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 7 \\ x=4.(7)-36=-8\end{matrix}\right.\\ \qquad V=\{(-8,7)\}\)
  9. \(\left\{\begin{matrix}x-4y=39\\4x-5y=68\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=4y+39\\ 4x-5y=68\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=4y+39\\ 4.\left(4y+39\right)-5y=68\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=4y+39\\ 16y+156-5y=68\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=4y+39\\ 11y=68-156=-88\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=4y+39\\ y=\frac{-88}{11}=-8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=4.(-8)+39=7\\ y=-8\end{matrix}\right.\\ \qquad V=\{(7,-8)\}\)
  10. \(\left\{\begin{matrix}5y=-10+5x\\x+6y=-61\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+5y=-10\\x+6y=-61\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-5x+5y=-10\\ x=-6y-61\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-5\left(-6y-61\right)+5y=-10\\x=-6y-61\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}30y+305+5y=-10\\x=-6y-61\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}35y=-10-305=-315\\x=-6y-61\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-315}{35} = -9 \\ x=-6y-61\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -9 \\ x=-6.(-9)-61=-7\end{matrix}\right.\\ \qquad V=\{(-7,-9)\}\)
  11. \(\left\{\begin{matrix}5x-6y=-7\\x=-3y-14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-6y=-7\\x+3y=-14\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}5x-6y=-7\\ x=-3y-14\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}5\left(-3y-14\right)-6y=-7\\x=-3y-14\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-15y-70-6y=-7\\x=-3y-14\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-21y=-7+70=63\\x=-3y-14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{63}{-21} = -3 \\ x=-3y-14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -3 \\ x=-3.(-3)-14=-5\end{matrix}\right.\\ \qquad V=\{(-5,-3)\}\)
  12. \(\left\{\begin{matrix}3x-5y=6\\4x-y=-9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-5y=6\\ 4x+9=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}3x-5\left(4x+9\right)=6\\y=4x+9\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}3x-20x-45=6\\y=4x+9\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-17x=6+45=51\\y=4x+9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{51}{-17} = -3 \\ y=4x+9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -3 \\ y=4.(-3)+9=-3\end{matrix}\right.\\ \qquad V=\{(-3,-3)\}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-20 16:06:08
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