Stelsels substitutie

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Substitutie

  1. \(\left\{\begin{matrix}-5x-4y=62\\x=-5y-25\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}3y=17+x\\5x+4y=10\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}x-6y=50\\5x=4y+42\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}4x-3y=46\\5x=-y+48\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}6y=32-2x\\-x+4y=40\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-2x+4y=-12\\-x=6y+58\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}6x+5y=-43\\6x=y-49\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-3x+4y=15\\6x-y=-9\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}x+4y=13\\-6x=-3y-24\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-x+y=5\\6x=-2y-70\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}4y=-30-6x\\3x+y=-12\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-5x+2y=33\\-5x+y=34\end{matrix}\right.\)

Substitutie

Verbetersleutel

  1. \(\left\{\begin{matrix}-5x-4y=62\\x=-5y-25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-4y=62\\x+5y=-25\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-5x-4y=62\\ x=-5y-25\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-5\left(-5y-25\right)-4y=62\\x=-5y-25\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}25y+125-4y=62\\x=-5y-25\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}21y=62-125=-63\\x=-5y-25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-63}{21} = -3 \\ x=-5y-25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -3 \\ x=-5.(-3)-25=-10\end{matrix}\right.\\ \qquad V=\{(-10,-3)\}\)
  2. \(\left\{\begin{matrix}3y=17+x\\5x+4y=10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-x+3y=17\\5x+4y=10\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}3y-17=x\\5x+4y=10\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=3y-17\\ 5.\left(3y-17\right)+4y=10\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=3y-17\\ 15y-85+4y=10\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=3y-17\\ 19y=10+85=95\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=3y-17\\ y=\frac{95}{19}=5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=3.(5)-17=-2\\ y=5\end{matrix}\right.\\ \qquad V=\{(-2,5)\}\)
  3. \(\left\{\begin{matrix}x-6y=50\\5x=4y+42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x-6y=50\\5x-4y=42\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}x=6y+50\\ 5x-4y=42\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=6y+50\\ 5.\left(6y+50\right)-4y=42\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=6y+50\\ 30y+250-4y=42\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=6y+50\\ 26y=42-250=-208\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=6y+50\\ y=\frac{-208}{26}=-8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=6.(-8)+50=2\\ y=-8\end{matrix}\right.\\ \qquad V=\{(2,-8)\}\)
  4. \(\left\{\begin{matrix}4x-3y=46\\5x=-y+48\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-3y=46\\5x+y=48\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}4x-3y=46\\ y=-5x+48\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}4x-3\left(-5x+48\right)=46\\y=-5x+48\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}4x+15x-144=46\\y=-5x+48\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}19x=46+144=190\\y=-5x+48\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{190}{19} = 10 \\ y=-5x+48\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 10 \\ y=-5.(10)+48=-2\end{matrix}\right.\\ \qquad V=\{(10,-2)\}\)
  5. \(\left\{\begin{matrix}6y=32-2x\\-x+4y=40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+6y=32\\-x+4y=40\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}2x+6y=32\\ 4y-40=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}2\left(4y-40\right)+6y=32\\x=4y-40\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}8y-80+6y=32\\x=4y-40\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}14y=32+80=112\\x=4y-40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{112}{14} = 8 \\ x=4y-40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 8 \\ x=4.(8)-40=-8\end{matrix}\right.\\ \qquad V=\{(-8,8)\}\)
  6. \(\left\{\begin{matrix}-2x+4y=-12\\-x=6y+58\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+4y=-12\\-x-6y=58\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-2x+4y=-12\\ -6y-58=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-2\left(-6y-58\right)+4y=-12\\x=-6y-58\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}12y+116+4y=-12\\x=-6y-58\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}16y=-12-116=-128\\x=-6y-58\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{-128}{16} = -8 \\ x=-6y-58\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -8 \\ x=-6.(-8)-58=-10\end{matrix}\right.\\ \qquad V=\{(-10,-8)\}\)
  7. \(\left\{\begin{matrix}6x+5y=-43\\6x=y-49\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+5y=-43\\6x-y=-49\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}6x+5y=-43\\ 6x+49=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}6x+5\left(6x+49\right)=-43\\y=6x+49\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}6x+30x+245=-43\\y=6x+49\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}36x=-43-245=-288\\y=6x+49\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-288}{36} = -8 \\ y=6x+49\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -8 \\ y=6.(-8)+49=1\end{matrix}\right.\\ \qquad V=\{(-8,1)\}\)
  8. \(\left\{\begin{matrix}-3x+4y=15\\6x-y=-9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+4y=15\\ 6x+9=y\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-3x+4\left(6x+9\right)=15\\y=6x+9\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-3x+24x+36=15\\y=6x+9\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}21x=15-36=-21\\y=6x+9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-21}{21} = -1 \\ y=6x+9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -1 \\ y=6.(-1)+9=3\end{matrix}\right.\\ \qquad V=\{(-1,3)\}\)
  9. \(\left\{\begin{matrix}x+4y=13\\-6x=-3y-24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x+4y=13\\-6x+3y=-24\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+13\\ -6x+3y=-24\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+13\\ -6.\left(-4y+13\right)+3y=-24\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+13\\ 24y-78+3y=-24\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+13\\ 27y=-24+78=54\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-4y+13\\ y=\frac{54}{27}=2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-4.(2)+13=5\\ y=2\end{matrix}\right.\\ \qquad V=\{(5,2)\}\)
  10. \(\left\{\begin{matrix}-x+y=5\\6x=-2y-70\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-x+y=5\\6x+2y=-70\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}y-5=x\\6x+2y=-70\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=y-5\\ 6.\left(y-5\right)+2y=-70\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=y-5\\ 6y-30+2y=-70\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=y-5\\ 8y=-70+30=-40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=y-5\\ y=\frac{-40}{8}=-5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=.(-5)-5=-10\\ y=-5\end{matrix}\right.\\ \qquad V=\{(-10,-5)\}\)
  11. \(\left\{\begin{matrix}4y=-30-6x\\3x+y=-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+4y=-30\\3x+y=-12\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}6x+4y=-30\\ y=-3x-12\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}6x+4\left(-3x-12\right)=-30\\y=-3x-12\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}6x-12x-48=-30\\y=-3x-12\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-6x=-30+48=18\\y=-3x-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{18}{-6} = -3 \\ y=-3x-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -3 \\ y=-3.(-3)-12=-3\end{matrix}\right.\\ \qquad V=\{(-3,-3)\}\)
  12. \(\left\{\begin{matrix}-5x+2y=33\\-5x+y=34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+2y=33\\ y=5x+34\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-5x+2\left(5x+34\right)=33\\y=5x+34\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-5x+10x+68=33\\y=5x+34\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}5x=33-68=-35\\y=5x+34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-35}{5} = -7 \\ y=5x+34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = -7 \\ y=5.(-7)+34=-1\end{matrix}\right.\\ \qquad V=\{(-7,-1)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-08 06:21:20