Stelsels substitutie

Hoofdmenu Eentje per keer 

Substitutie

  1. \(\left\{\begin{matrix}6y=-14-4x\\-2x-y=13\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}6x-4y=26\\x=2y-1\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}y=-14+2x\\2x+2y=-4\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-4x+3y=-29\\4x+y=1\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-4x-3y=31\\-x-4y=-2\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}6y=10+5x\\-4x-y=37\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}5y=68+6x\\2x+y=-12\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}4x-2y=-12\\-x=3y+38\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}6x+2y=-2\\5x=y+17\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}2x+4y=-14\\-5x=y-28\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}3x-4y=10\\x-3y=20\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}x+4y=20\\-3x=3y-24\end{matrix}\right.\)

Substitutie

Verbetersleutel

  1. \(\left\{\begin{matrix}6y=-14-4x\\-2x-y=13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+6y=-14\\-2x-y=13\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}4x+6y=-14\\ -2x-13=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}4x+6\left(-2x-13\right)=-14\\y=-2x-13\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}4x-12x-78=-14\\y=-2x-13\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-8x=-14+78=64\\y=-2x-13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{64}{-8} = -8 \\ y=-2x-13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -8 \\ y=-2.(-8)-13=3\end{matrix}\right.\\ \qquad V=\{(-8,3)\}\)
  2. \(\left\{\begin{matrix}6x-4y=26\\x=2y-1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x-4y=26\\x-2y=-1\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}6x-4y=26\\ x=2y-1\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}6\left(2y-1\right)-4y=26\\x=2y-1\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}12y-6-4y=26\\x=2y-1\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}8y=26+6=32\\x=2y-1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{32}{8} = 4 \\ x=2y-1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 4 \\ x=2.(4)-1=7\end{matrix}\right.\\ \qquad V=\{(7,4)\}\)
  3. \(\left\{\begin{matrix}y=-14+2x\\2x+2y=-4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+y=-14\\2x+2y=-4\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}y=2x-14\\ 2x+2y=-4\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}y=2x-14\\ 2x+2\left(2x-14\right)=-4\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}y=2x-14\\ 2x+4x-28=-4\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}y=2x-14\\ 6x=-4+28=24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=2x-14\\ x=\frac{24}{6}=4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=2.(4)-14=-6\\ x=4\end{matrix}\right.\\ \qquad V=\{(4,-6)\}\)
  4. \(\left\{\begin{matrix}-4x+3y=-29\\4x+y=1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+3y=-29\\ y=-4x+1\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-4x+3\left(-4x+1\right)=-29\\y=-4x+1\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-4x-12x+3=-29\\y=-4x+1\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-16x=-29-3=-32\\y=-4x+1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-32}{-16} = 2 \\ y=-4x+1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 2 \\ y=-4.(2)+1=-7\end{matrix}\right.\\ \qquad V=\{(2,-7)\}\)
  5. \(\left\{\begin{matrix}-4x-3y=31\\-x-4y=-2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-3y=31\\ -4y+2=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-4\left(-4y+2\right)-3y=31\\x=-4y+2\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}16y-8-3y=31\\x=-4y+2\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}13y=31+8=39\\x=-4y+2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{39}{13} = 3 \\ x=-4y+2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 3 \\ x=-4.(3)+2=-10\end{matrix}\right.\\ \qquad V=\{(-10,3)\}\)
  6. \(\left\{\begin{matrix}6y=10+5x\\-4x-y=37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+6y=10\\-4x-y=37\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-5x+6y=10\\ -4x-37=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-5x+6\left(-4x-37\right)=10\\y=-4x-37\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-5x-24x-222=10\\y=-4x-37\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-29x=10+222=232\\y=-4x-37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{232}{-29} = -8 \\ y=-4x-37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -8 \\ y=-4.(-8)-37=-5\end{matrix}\right.\\ \qquad V=\{(-8,-5)\}\)
  7. \(\left\{\begin{matrix}5y=68+6x\\2x+y=-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+5y=68\\2x+y=-12\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-6x+5y=68\\ y=-2x-12\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-6x+5\left(-2x-12\right)=68\\y=-2x-12\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-6x-10x-60=68\\y=-2x-12\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-16x=68+60=128\\y=-2x-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{128}{-16} = -8 \\ y=-2x-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -8 \\ y=-2.(-8)-12=4\end{matrix}\right.\\ \qquad V=\{(-8,4)\}\)
  8. \(\left\{\begin{matrix}4x-2y=-12\\-x=3y+38\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-2y=-12\\-x-3y=38\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}4x-2y=-12\\ -3y-38=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}4\left(-3y-38\right)-2y=-12\\x=-3y-38\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-12y-152-2y=-12\\x=-3y-38\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-14y=-12+152=140\\x=-3y-38\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{140}{-14} = -10 \\ x=-3y-38\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -10 \\ x=-3.(-10)-38=-8\end{matrix}\right.\\ \qquad V=\{(-8,-10)\}\)
  9. \(\left\{\begin{matrix}6x+2y=-2\\5x=y+17\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+2y=-2\\5x-y=17\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}6x+2y=-2\\ 5x-17=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}6x+2\left(5x-17\right)=-2\\y=5x-17\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}6x+10x-34=-2\\y=5x-17\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}16x=-2+34=32\\y=5x-17\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{32}{16} = 2 \\ y=5x-17\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 2 \\ y=5.(2)-17=-7\end{matrix}\right.\\ \qquad V=\{(2,-7)\}\)
  10. \(\left\{\begin{matrix}2x+4y=-14\\-5x=y-28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+4y=-14\\-5x-y=-28\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}2x+4y=-14\\ -5x+28=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}2x+4\left(-5x+28\right)=-14\\y=-5x+28\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}2x-20x+112=-14\\y=-5x+28\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-18x=-14-112=-126\\y=-5x+28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-126}{-18} = 7 \\ y=-5x+28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 7 \\ y=-5.(7)+28=-7\end{matrix}\right.\\ \qquad V=\{(7,-7)\}\)
  11. \(\left\{\begin{matrix}3x-4y=10\\x-3y=20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-4y=10\\ x=3y+20\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}3\left(3y+20\right)-4y=10\\x=3y+20\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}9y+60-4y=10\\x=3y+20\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}5y=10-60=-50\\x=3y+20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-50}{5} = -10 \\ x=3y+20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -10 \\ x=3.(-10)+20=-10\end{matrix}\right.\\ \qquad V=\{(-10,-10)\}\)
  12. \(\left\{\begin{matrix}x+4y=20\\-3x=3y-24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x+4y=20\\-3x-3y=-24\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+20\\ -3x-3y=-24\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+20\\ -3.\left(-4y+20\right)-3y=-24\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+20\\ 12y-60-3y=-24\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+20\\ 9y=-24+60=36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+20\\ y=\frac{36}{9}=4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-4.(4)+20=4\\ y=4\end{matrix}\right.\\ \qquad V=\{(4,4)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-05-19 05:04:41