Stelsels substitutie

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Substitutie

  1. \(\left\{\begin{matrix}6y=-58-4x\\-x+2y=-10\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}4y=12-x\\2x+3y=14\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}5y=-43-x\\-6x+3y=-6\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-2x+5y=17\\-3x+y=19\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-3y=-33-2x\\2x+y=3\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-5y=-85-5x\\-2x+y=26\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-6y=31-x\\4x-2y=-8\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-6y=-36-6x\\-3x-y=34\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}6y=30+6x\\x-2y=-6\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-6y=-6-3x\\3x-y=24\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}x-y=-4\\-2x+3y=6\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}2y=-32-2x\\-x-6y=66\end{matrix}\right.\)

Substitutie

Verbetersleutel

  1. \(\left\{\begin{matrix}6y=-58-4x\\-x+2y=-10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+6y=-58\\-x+2y=-10\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}4x+6y=-58\\ 2y+10=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}4\left(2y+10\right)+6y=-58\\x=2y+10\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}8y+40+6y=-58\\x=2y+10\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}14y=-58-40=-98\\x=2y+10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-98}{14} = -7 \\ x=2y+10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -7 \\ x=2.(-7)+10=-4\end{matrix}\right.\\ \qquad V=\{(-4,-7)\}\)
  2. \(\left\{\begin{matrix}4y=12-x\\2x+3y=14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x+4y=12\\2x+3y=14\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+12\\ 2x+3y=14\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+12\\ 2.\left(-4y+12\right)+3y=14\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+12\\ -8y+24+3y=14\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+12\\ -5y=14-24=-10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+12\\ y=\frac{-10}{-5}=2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-4.(2)+12=4\\ y=2\end{matrix}\right.\\ \qquad V=\{(4,2)\}\)
  3. \(\left\{\begin{matrix}5y=-43-x\\-6x+3y=-6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x+5y=-43\\-6x+3y=-6\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}x=-5y-43\\ -6x+3y=-6\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=-5y-43\\ -6.\left(-5y-43\right)+3y=-6\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=-5y-43\\ 30y+258+3y=-6\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=-5y-43\\ 33y=-6-258=-264\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-5y-43\\ y=\frac{-264}{33}=-8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-5.(-8)-43=-3\\ y=-8\end{matrix}\right.\\ \qquad V=\{(-3,-8)\}\)
  4. \(\left\{\begin{matrix}-2x+5y=17\\-3x+y=19\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+5y=17\\ y=3x+19\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-2x+5\left(3x+19\right)=17\\y=3x+19\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-2x+15x+95=17\\y=3x+19\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}13x=17-95=-78\\y=3x+19\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-78}{13} = -6 \\ y=3x+19\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -6 \\ y=3.(-6)+19=1\end{matrix}\right.\\ \qquad V=\{(-6,1)\}\)
  5. \(\left\{\begin{matrix}-3y=-33-2x\\2x+y=3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x-3y=-33\\2x+y=3\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}2x-3y=-33\\ y=-2x+3\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}2x-3\left(-2x+3\right)=-33\\y=-2x+3\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}2x+6x-9=-33\\y=-2x+3\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}8x=-33+9=-24\\y=-2x+3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-24}{8} = -3 \\ y=-2x+3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -3 \\ y=-2.(-3)+3=9\end{matrix}\right.\\ \qquad V=\{(-3,9)\}\)
  6. \(\left\{\begin{matrix}-5y=-85-5x\\-2x+y=26\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-5y=-85\\-2x+y=26\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}5x-5y=-85\\ y=2x+26\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}5x-5\left(2x+26\right)=-85\\y=2x+26\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}5x-10x-130=-85\\y=2x+26\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-5x=-85+130=45\\y=2x+26\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{45}{-5} = -9 \\ y=2x+26\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -9 \\ y=2.(-9)+26=8\end{matrix}\right.\\ \qquad V=\{(-9,8)\}\)
  7. \(\left\{\begin{matrix}-6y=31-x\\4x-2y=-8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x-6y=31\\4x-2y=-8\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}x=6y+31\\ 4x-2y=-8\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=6y+31\\ 4.\left(6y+31\right)-2y=-8\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=6y+31\\ 24y+124-2y=-8\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=6y+31\\ 22y=-8-124=-132\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=6y+31\\ y=\frac{-132}{22}=-6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=6.(-6)+31=-5\\ y=-6\end{matrix}\right.\\ \qquad V=\{(-5,-6)\}\)
  8. \(\left\{\begin{matrix}-6y=-36-6x\\-3x-y=34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x-6y=-36\\-3x-y=34\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}6x-6y=-36\\ -3x-34=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}6x-6\left(-3x-34\right)=-36\\y=-3x-34\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}6x+18x+204=-36\\y=-3x-34\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}24x=-36-204=-240\\y=-3x-34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-240}{24} = -10 \\ y=-3x-34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -10 \\ y=-3.(-10)-34=-4\end{matrix}\right.\\ \qquad V=\{(-10,-4)\}\)
  9. \(\left\{\begin{matrix}6y=30+6x\\x-2y=-6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+6y=30\\x-2y=-6\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-6x+6y=30\\ x=2y-6\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-6\left(2y-6\right)+6y=30\\x=2y-6\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-12y+36+6y=30\\x=2y-6\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-6y=30-36=-6\\x=2y-6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-6}{-6} = 1 \\ x=2y-6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 1 \\ x=2.(1)-6=-4\end{matrix}\right.\\ \qquad V=\{(-4,1)\}\)
  10. \(\left\{\begin{matrix}-6y=-6-3x\\3x-y=24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-6y=-6\\3x-y=24\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}3x-6y=-6\\ 3x-24=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}3x-6\left(3x-24\right)=-6\\y=3x-24\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}3x-18x+144=-6\\y=3x-24\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-15x=-6-144=-150\\y=3x-24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-150}{-15} = 10 \\ y=3x-24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 10 \\ y=3.(10)-24=6\end{matrix}\right.\\ \qquad V=\{(10,6)\}\)
  11. \(\left\{\begin{matrix}x-y=-4\\-2x+3y=6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=y-4\\ -2x+3y=6\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=y-4\\ -2.\left(y-4\right)+3y=6\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=y-4\\ -2y+8+3y=6\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=y-4\\ y=6-8=-2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=y-4\\ y=\frac{-2}{1}=-2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=.(-2)-4=-6\\ y=-2\end{matrix}\right.\\ \qquad V=\{(-6,-2)\}\)
  12. \(\left\{\begin{matrix}2y=-32-2x\\-x-6y=66\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+2y=-32\\-x-6y=66\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}2x+2y=-32\\ -6y-66=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}2\left(-6y-66\right)+2y=-32\\x=-6y-66\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-12y-132+2y=-32\\x=-6y-66\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-10y=-32+132=100\\x=-6y-66\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{100}{-10} = -10 \\ x=-6y-66\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -10 \\ x=-6.(-10)-66=-6\end{matrix}\right.\\ \qquad V=\{(-6,-10)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-12-14 05:51:28