Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}3x+8y=-60\\-2x=6y+46\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}8x-5y=53\\10y-10x=-100\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}10x-6y=24\\-4y-7x=-25\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}9y=-106+2x\\4x-3y=62\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}5x+10y=-80\\-3x=-2y-8\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}10x-7y=16\\-5x=5y-25\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-2x+8y=-98\\6x+9y=-36\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}9x+2y=50\\-9x+10y=34\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}-2x+2y=-16\\4x=-8y+56\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}7x+4y=54\\-3y+2x=32\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}9x-3y=-84\\4x+8y=56\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}5y=65+2x\\-2x+6y=74\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}3x+8y=-60\\-2x=6y+46\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+8y=-60\\-2x-6y=46\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+8y=-60& \color{red}{2.} & \color{blue}{3.} \\-2x-6y=46& \color{red}{3.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}+16y-18y=-120+138} \\ \color{blue}{9x-8x\underline{+24y-24y}=-180+184} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2y=18 \\x=4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{18}{-2}=-9 \\x=\frac{4}{1}=4\end{matrix}\right.\\ \qquad V=\{(4,-9)\}\)
  2. \(\left\{\begin{matrix}8x-5y=53\\10y-10x=-100\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x-5y=53\\-10x+10y=-100\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-5y=53& \color{red}{5.} & \color{blue}{2.} \\-10x+10y=-100& \color{red}{4.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}-25y+40y=265-400} \\ \color{blue}{16x-10x\underline{-10y+10y}=106-100} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}15y=-135 \\6x=6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-135}{15}=-9 \\x=\frac{6}{6}=1\end{matrix}\right.\\ \qquad V=\{(1,-9)\}\)
  3. \(\left\{\begin{matrix}10x-6y=24\\-4y-7x=-25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x-6y=24\\-7x-4y=-25\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-6y=24& \color{red}{7.} & \color{blue}{2.} \\-7x-4y=-25& \color{red}{10.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{70x-70x}-42y-40y=168-250} \\ \color{blue}{20x+21x\underline{-12y+12y}=48+75} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-82y=-82 \\41x=123\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-82}{-82}=1 \\x=\frac{123}{41}=3\end{matrix}\right.\\ \qquad V=\{(3,1)\}\)
  4. \(\left\{\begin{matrix}9y=-106+2x\\4x-3y=62\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+9y=-106\\4x-3y=62\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+9y=-106& \color{red}{2.} & \color{blue}{1.} \\4x-3y=62& \color{red}{1.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-4x+4x}+18y-3y=-212+62} \\ \color{blue}{-2x+12x\underline{+9y-9y}=-106+186} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}15y=-150 \\10x=80\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-150}{15}=-10 \\x=\frac{80}{10}=8\end{matrix}\right.\\ \qquad V=\{(8,-10)\}\)
  5. \(\left\{\begin{matrix}5x+10y=-80\\-3x=-2y-8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x+10y=-80\\-3x+2y=-8\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x+10y=-80& \color{red}{3.} & \color{blue}{1.} \\-3x+2y=-8& \color{red}{5.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{15x-15x}+30y+10y=-240-40} \\ \color{blue}{5x+15x\underline{+10y-10y}=-80+40} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}40y=-280 \\20x=-40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-280}{40}=-7 \\x=\frac{-40}{20}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-7)\}\)
  6. \(\left\{\begin{matrix}10x-7y=16\\-5x=5y-25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x-7y=16\\-5x-5y=-25\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-7y=16& \color{red}{1.} & \color{blue}{5.} \\-5x-5y=-25& \color{red}{2.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-7y-10y=16-50} \\ \color{blue}{50x+35x\underline{-35y+35y}=80+175} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-17y=-34 \\85x=255\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-34}{-17}=2 \\x=\frac{255}{85}=3\end{matrix}\right.\\ \qquad V=\{(3,2)\}\)
  7. \(\left\{\begin{matrix}-2x+8y=-98\\6x+9y=-36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+8y=-98& \color{red}{3.} & \color{blue}{9.} \\6x+9y=-36& \color{red}{1.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+24y+9y=-294-36} \\ \color{blue}{-18x-48x\underline{+72y-72y}=-882+288} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}33y=-330 \\-66x=-594\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-330}{33}=-10 \\x=\frac{-594}{-66}=9\end{matrix}\right.\\ \qquad V=\{(9,-10)\}\)
  8. \(\left\{\begin{matrix}9x+2y=50\\-9x+10y=34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+2y=50& \color{red}{1.} & \color{blue}{5.} \\-9x+10y=34& \color{red}{1.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{9x-9x}+2y+10y=50+34} \\ \color{blue}{45x+9x\underline{+10y-10y}=250-34} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}12y=84 \\54x=216\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{84}{12}=7 \\x=\frac{216}{54}=4\end{matrix}\right.\\ \qquad V=\{(4,7)\}\)
  9. \(\left\{\begin{matrix}-2x+2y=-16\\4x=-8y+56\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+2y=-16\\4x+8y=56\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+2y=-16& \color{red}{2.} & \color{blue}{4.} \\4x+8y=56& \color{red}{1.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-4x+4x}+4y+8y=-32+56} \\ \color{blue}{-8x-4x\underline{+8y-8y}=-64-56} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}12y=24 \\-12x=-120\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{24}{12}=2 \\x=\frac{-120}{-12}=10\end{matrix}\right.\\ \qquad V=\{(10,2)\}\)
  10. \(\left\{\begin{matrix}7x+4y=54\\-3y+2x=32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+4y=54\\2x-3y=32\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+4y=54& \color{red}{2.} & \color{blue}{3.} \\2x-3y=32& \color{red}{-7.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{14x-14x}+8y+21y=108-224} \\ \color{blue}{21x+8x\underline{+12y-12y}=162+128} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}29y=-116 \\29x=290\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-116}{29}=-4 \\x=\frac{290}{29}=10\end{matrix}\right.\\ \qquad V=\{(10,-4)\}\)
  11. \(\left\{\begin{matrix}9x-3y=-84\\4x+8y=56\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x-3y=-84& \color{red}{4.} & \color{blue}{8.} \\4x+8y=56& \color{red}{-9.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{36x-36x}-12y-72y=-336-504} \\ \color{blue}{72x+12x\underline{-24y+24y}=-672+168} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-84y=-840 \\84x=-504\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-840}{-84}=10 \\x=\frac{-504}{84}=-6\end{matrix}\right.\\ \qquad V=\{(-6,10)\}\)
  12. \(\left\{\begin{matrix}5y=65+2x\\-2x+6y=74\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+5y=65\\-2x+6y=74\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+5y=65& \color{red}{1.} & \color{blue}{6.} \\-2x+6y=74& \color{red}{-1.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-2x+2x}+5y-6y=65-74} \\ \color{blue}{-12x+10x\underline{+30y-30y}=390-370} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-y=-9 \\-2x=20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-9}{-1}=9 \\x=\frac{20}{-2}=-10\end{matrix}\right.\\ \qquad V=\{(-10,9)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-11-23 09:01:51