Stelsels substitutie

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Substitutie

  1. \(\left\{\begin{matrix}-2x+4y=14\\-3x+y=-9\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}2x-5y=-44\\-x=3y-33\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}4x-4y=24\\x+2y=9\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}4x-5y=-24\\-x+2y=9\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-4y=25+3x\\x-5y=55\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-6x+4y=-26\\3x-y=14\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}6y=-5-5x\\-x+3y=22\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-2x-6y=30\\-5x-y=-23\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}3x+5y=-25\\-x-6y=17\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-5x+2y=10\\x=3y-28\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}2x+y=12\\4x+4y=44\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}2x+5y=-36\\x=-6y-53\end{matrix}\right.\)

Substitutie

Verbetersleutel

  1. \(\left\{\begin{matrix}-2x+4y=14\\-3x+y=-9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+4y=14\\ y=3x-9\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-2x+4\left(3x-9\right)=14\\y=3x-9\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-2x+12x-36=14\\y=3x-9\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}10x=14+36=50\\y=3x-9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{50}{10} = 5 \\ y=3x-9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 5 \\ y=3.(5)-9=6\end{matrix}\right.\\ \qquad V=\{(5,6)\}\)
  2. \(\left\{\begin{matrix}2x-5y=-44\\-x=3y-33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x-5y=-44\\-x-3y=-33\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}2x-5y=-44\\ -3y+33=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}2\left(-3y+33\right)-5y=-44\\x=-3y+33\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-6y+66-5y=-44\\x=-3y+33\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-11y=-44-66=-110\\x=-3y+33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-110}{-11} = 10 \\ x=-3y+33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 10 \\ x=-3.(10)+33=3\end{matrix}\right.\\ \qquad V=\{(3,10)\}\)
  3. \(\left\{\begin{matrix}4x-4y=24\\x+2y=9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-4y=24\\ x=-2y+9\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}4\left(-2y+9\right)-4y=24\\x=-2y+9\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-8y+36-4y=24\\x=-2y+9\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-12y=24-36=-12\\x=-2y+9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-12}{-12} = 1 \\ x=-2y+9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 1 \\ x=-2.(1)+9=7\end{matrix}\right.\\ \qquad V=\{(7,1)\}\)
  4. \(\left\{\begin{matrix}4x-5y=-24\\-x+2y=9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-5y=-24\\ 2y-9=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}4\left(2y-9\right)-5y=-24\\x=2y-9\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}8y-36-5y=-24\\x=2y-9\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}3y=-24+36=12\\x=2y-9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{12}{3} = 4 \\ x=2y-9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 4 \\ x=2.(4)-9=-1\end{matrix}\right.\\ \qquad V=\{(-1,4)\}\)
  5. \(\left\{\begin{matrix}-4y=25+3x\\x-5y=55\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x-4y=25\\x-5y=55\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-3x-4y=25\\ x=5y+55\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-3\left(5y+55\right)-4y=25\\x=5y+55\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-15y-165-4y=25\\x=5y+55\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-19y=25+165=190\\x=5y+55\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{190}{-19} = -10 \\ x=5y+55\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -10 \\ x=5.(-10)+55=5\end{matrix}\right.\\ \qquad V=\{(5,-10)\}\)
  6. \(\left\{\begin{matrix}-6x+4y=-26\\3x-y=14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+4y=-26\\ 3x-14=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-6x+4\left(3x-14\right)=-26\\y=3x-14\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-6x+12x-56=-26\\y=3x-14\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}6x=-26+56=30\\y=3x-14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{30}{6} = 5 \\ y=3x-14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 5 \\ y=3.(5)-14=1\end{matrix}\right.\\ \qquad V=\{(5,1)\}\)
  7. \(\left\{\begin{matrix}6y=-5-5x\\-x+3y=22\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x+6y=-5\\-x+3y=22\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}5x+6y=-5\\ 3y-22=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}5\left(3y-22\right)+6y=-5\\x=3y-22\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}15y-110+6y=-5\\x=3y-22\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}21y=-5+110=105\\x=3y-22\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{105}{21} = 5 \\ x=3y-22\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 5 \\ x=3.(5)-22=-7\end{matrix}\right.\\ \qquad V=\{(-7,5)\}\)
  8. \(\left\{\begin{matrix}-2x-6y=30\\-5x-y=-23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-6y=30\\ -5x+23=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-2x-6\left(-5x+23\right)=30\\y=-5x+23\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-2x+30x-138=30\\y=-5x+23\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}28x=30+138=168\\y=-5x+23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{168}{28} = 6 \\ y=-5x+23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 6 \\ y=-5.(6)+23=-7\end{matrix}\right.\\ \qquad V=\{(6,-7)\}\)
  9. \(\left\{\begin{matrix}3x+5y=-25\\-x-6y=17\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+5y=-25\\ -6y-17=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}3\left(-6y-17\right)+5y=-25\\x=-6y-17\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-18y-51+5y=-25\\x=-6y-17\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-13y=-25+51=26\\x=-6y-17\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{26}{-13} = -2 \\ x=-6y-17\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -2 \\ x=-6.(-2)-17=-5\end{matrix}\right.\\ \qquad V=\{(-5,-2)\}\)
  10. \(\left\{\begin{matrix}-5x+2y=10\\x=3y-28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+2y=10\\x-3y=-28\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-5x+2y=10\\ x=3y-28\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-5\left(3y-28\right)+2y=10\\x=3y-28\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-15y+140+2y=10\\x=3y-28\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-13y=10-140=-130\\x=3y-28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-130}{-13} = 10 \\ x=3y-28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 10 \\ x=3.(10)-28=2\end{matrix}\right.\\ \qquad V=\{(2,10)\}\)
  11. \(\left\{\begin{matrix}2x+y=12\\4x+4y=44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-2x+12\\ 4x+4y=44\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}y=-2x+12\\ 4x+4\left(-2x+12\right)=44\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}y=-2x+12\\ 4x-8x+48=44\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}y=-2x+12\\ -4x=44-48=-4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-2x+12\\ x=\frac{-4}{-4}=1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-2.(1)+12=10\\ x=1\end{matrix}\right.\\ \qquad V=\{(1,10)\}\)
  12. \(\left\{\begin{matrix}2x+5y=-36\\x=-6y-53\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+5y=-36\\x+6y=-53\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}2x+5y=-36\\ x=-6y-53\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}2\left(-6y-53\right)+5y=-36\\x=-6y-53\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-12y-106+5y=-36\\x=-6y-53\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-7y=-36+106=70\\x=-6y-53\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{70}{-7} = -10 \\ x=-6y-53\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -10 \\ x=-6.(-10)-53=7\end{matrix}\right.\\ \qquad V=\{(7,-10)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2026-06-18 10:14:30