Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}-8x+6y=-24\\6x-4y=20\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}6y-5x=-76\\8x+5y=34\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}-6x+7y=-84\\9x=2y+75\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}6x-10y=-80\\9x=7y-104\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-9x-3y=-36\\6x-7y=-30\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}9y+6x=-114\\6x-3y=6\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-2x+5y=21\\10y-5x=40\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-5x-2y=-50\\3y+4x=47\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}10y+10x=0\\-2x-7y=-20\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}4x-4y=8\\-7y+3x=-6\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}-7y+3x=41\\-9x+3y=-87\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}7y=-30-8x\\-7x-3y=-5\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}-8x+6y=-24\\6x-4y=20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+6y=-24& \color{red}{3.} & \color{blue}{2.} \\6x-4y=20& \color{red}{4.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}+18y-16y=-72+80} \\ \color{blue}{-16x+18x\underline{+12y-12y}=-48+60} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2y=8 \\2x=12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{8}{2}=4 \\x=\frac{12}{2}=6\end{matrix}\right.\\ \qquad V=\{(6,4)\}\)
  2. \(\left\{\begin{matrix}6y-5x=-76\\8x+5y=34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+6y=-76\\8x+5y=34\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x+6y=-76& \color{red}{8.} & \color{blue}{5.} \\8x+5y=34& \color{red}{5.} & \color{blue}{-6.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-40x+40x}+48y+25y=-608+170} \\ \color{blue}{-25x-48x\underline{+30y-30y}=-380-204} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}73y=-438 \\-73x=-584\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-438}{73}=-6 \\x=\frac{-584}{-73}=8\end{matrix}\right.\\ \qquad V=\{(8,-6)\}\)
  3. \(\left\{\begin{matrix}-6x+7y=-84\\9x=2y+75\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+7y=-84\\9x-2y=75\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+7y=-84& \color{red}{3.} & \color{blue}{2.} \\9x-2y=75& \color{red}{2.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}+21y-4y=-252+150} \\ \color{blue}{-12x+63x\underline{+14y-14y}=-168+525} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}17y=-102 \\51x=357\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-102}{17}=-6 \\x=\frac{357}{51}=7\end{matrix}\right.\\ \qquad V=\{(7,-6)\}\)
  4. \(\left\{\begin{matrix}6x-10y=-80\\9x=7y-104\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x-10y=-80\\9x-7y=-104\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-10y=-80& \color{red}{3.} & \color{blue}{7.} \\9x-7y=-104& \color{red}{-2.} & \color{blue}{-10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{18x-18x}-30y+14y=-240+208} \\ \color{blue}{42x-90x\underline{-70y+70y}=-560+1040} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-16y=-32 \\-48x=480\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-32}{-16}=2 \\x=\frac{480}{-48}=-10\end{matrix}\right.\\ \qquad V=\{(-10,2)\}\)
  5. \(\left\{\begin{matrix}-9x-3y=-36\\6x-7y=-30\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x-3y=-36& \color{red}{2.} & \color{blue}{7.} \\6x-7y=-30& \color{red}{3.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}-6y-21y=-72-90} \\ \color{blue}{-63x-18x\underline{-21y+21y}=-252+90} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-27y=-162 \\-81x=-162\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-162}{-27}=6 \\x=\frac{-162}{-81}=2\end{matrix}\right.\\ \qquad V=\{(2,6)\}\)
  6. \(\left\{\begin{matrix}9y+6x=-114\\6x-3y=6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+9y=-114\\6x-3y=6\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x+9y=-114& \color{red}{1.} & \color{blue}{1.} \\6x-3y=6& \color{red}{-1.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}+9y+3y=-114-6} \\ \color{blue}{6x+18x\underline{+9y-9y}=-114+18} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}12y=-120 \\24x=-96\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-120}{12}=-10 \\x=\frac{-96}{24}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-10)\}\)
  7. \(\left\{\begin{matrix}-2x+5y=21\\10y-5x=40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+5y=21\\-5x+10y=40\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+5y=21& \color{red}{5.} & \color{blue}{2.} \\-5x+10y=40& \color{red}{-2.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}+25y-20y=105-80} \\ \color{blue}{-4x+5x\underline{+10y-10y}=42-40} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5y=25 \\x=2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{25}{5}=5 \\x=\frac{2}{1}=2\end{matrix}\right.\\ \qquad V=\{(2,5)\}\)
  8. \(\left\{\begin{matrix}-5x-2y=-50\\3y+4x=47\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-2y=-50\\4x+3y=47\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-2y=-50& \color{red}{4.} & \color{blue}{3.} \\4x+3y=47& \color{red}{5.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-20x+20x}-8y+15y=-200+235} \\ \color{blue}{-15x+8x\underline{-6y+6y}=-150+94} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7y=35 \\-7x=-56\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{35}{7}=5 \\x=\frac{-56}{-7}=8\end{matrix}\right.\\ \qquad V=\{(8,5)\}\)
  9. \(\left\{\begin{matrix}10y+10x=0\\-2x-7y=-20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x+10y=0\\-2x-7y=-20\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x+10y=0& \color{red}{1.} & \color{blue}{7.} \\-2x-7y=-20& \color{red}{5.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}+10y-35y=0-100} \\ \color{blue}{70x-20x\underline{+70y-70y}=0-200} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-25y=-100 \\50x=-200\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-100}{-25}=4 \\x=\frac{-200}{50}=-4\end{matrix}\right.\\ \qquad V=\{(-4,4)\}\)
  10. \(\left\{\begin{matrix}4x-4y=8\\-7y+3x=-6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-4y=8\\3x-7y=-6\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x-4y=8& \color{red}{3.} & \color{blue}{7.} \\3x-7y=-6& \color{red}{-4.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{12x-12x}-12y+28y=24+24} \\ \color{blue}{28x-12x\underline{-28y+28y}=56+24} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}16y=48 \\16x=80\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{48}{16}=3 \\x=\frac{80}{16}=5\end{matrix}\right.\\ \qquad V=\{(5,3)\}\)
  11. \(\left\{\begin{matrix}-7y+3x=41\\-9x+3y=-87\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-7y=41\\-9x+3y=-87\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-7y=41& \color{red}{3.} & \color{blue}{3.} \\-9x+3y=-87& \color{red}{1.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{9x-9x}-21y+3y=123-87} \\ \color{blue}{9x-63x\underline{-21y+21y}=123-609} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-18y=36 \\-54x=-486\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{36}{-18}=-2 \\x=\frac{-486}{-54}=9\end{matrix}\right.\\ \qquad V=\{(9,-2)\}\)
  12. \(\left\{\begin{matrix}7y=-30-8x\\-7x-3y=-5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x+7y=-30\\-7x-3y=-5\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+7y=-30& \color{red}{7.} & \color{blue}{3.} \\-7x-3y=-5& \color{red}{8.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{56x-56x}+49y-24y=-210-40} \\ \color{blue}{24x-49x\underline{+21y-21y}=-90-35} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}25y=-250 \\-25x=-125\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-250}{25}=-10 \\x=\frac{-125}{-25}=5\end{matrix}\right.\\ \qquad V=\{(5,-10)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-04-26 07:12:53