Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}5x+3y=-34\\5y+10x=-70\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}4x+4y=60\\-2x-6y=-50\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}-5y=35+10x\\6x+4y=-12\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-5x+5y=5\\9y-2x=37\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-4x-6y=-36\\-2y-8x=28\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-7x-5y=-21\\-7y-9x=-23\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-4y-10x=66\\3x+9y=-90\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-9x+7y=39\\-9y+2x=36\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}-6x-10y=-68\\6x-4y=-44\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-8x+2y=-44\\-3y-6x=-42\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}4x-4y=4\\7y-2x=13\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}10x-7y=-96\\8x-5y=-72\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}5x+3y=-34\\5y+10x=-70\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x+3y=-34\\10x+5y=-70\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x+3y=-34& \color{red}{2.} & \color{blue}{5.} \\10x+5y=-70& \color{red}{-1.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}+6y-5y=-68+70} \\ \color{blue}{25x-30x\underline{+15y-15y}=-170+210} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=2 \\-5x=40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{2}{1}=2 \\x=\frac{40}{-5}=-8\end{matrix}\right.\\ \qquad V=\{(-8,2)\}\)
  2. \(\left\{\begin{matrix}4x+4y=60\\-2x-6y=-50\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+4y=60& \color{red}{1.} & \color{blue}{3.} \\-2x-6y=-50& \color{red}{2.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{4x-4x}+4y-12y=60-100} \\ \color{blue}{12x-4x\underline{+12y-12y}=180-100} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8y=-40 \\8x=80\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-40}{-8}=5 \\x=\frac{80}{8}=10\end{matrix}\right.\\ \qquad V=\{(10,5)\}\)
  3. \(\left\{\begin{matrix}-5y=35+10x\\6x+4y=-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x-5y=35\\6x+4y=-12\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x-5y=35& \color{red}{3.} & \color{blue}{4.} \\6x+4y=-12& \color{red}{5.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}-15y+20y=105-60} \\ \color{blue}{-40x+30x\underline{-20y+20y}=140-60} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5y=45 \\-10x=80\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{45}{5}=9 \\x=\frac{80}{-10}=-8\end{matrix}\right.\\ \qquad V=\{(-8,9)\}\)
  4. \(\left\{\begin{matrix}-5x+5y=5\\9y-2x=37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+5y=5\\-2x+9y=37\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x+5y=5& \color{red}{2.} & \color{blue}{9.} \\-2x+9y=37& \color{red}{-5.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}+10y-45y=10-185} \\ \color{blue}{-45x+10x\underline{+45y-45y}=45-185} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-35y=-175 \\-35x=-140\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-175}{-35}=5 \\x=\frac{-140}{-35}=4\end{matrix}\right.\\ \qquad V=\{(4,5)\}\)
  5. \(\left\{\begin{matrix}-4x-6y=-36\\-2y-8x=28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-6y=-36\\-8x-2y=28\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x-6y=-36& \color{red}{2.} & \color{blue}{1.} \\-8x-2y=28& \color{red}{-1.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}-12y+2y=-72-28} \\ \color{blue}{-4x+24x\underline{-6y+6y}=-36-84} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10y=-100 \\20x=-120\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-100}{-10}=10 \\x=\frac{-120}{20}=-6\end{matrix}\right.\\ \qquad V=\{(-6,10)\}\)
  6. \(\left\{\begin{matrix}-7x-5y=-21\\-7y-9x=-23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-5y=-21\\-9x-7y=-23\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-5y=-21& \color{red}{9.} & \color{blue}{7.} \\-9x-7y=-23& \color{red}{-7.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-63x+63x}-45y+49y=-189+161} \\ \color{blue}{-49x+45x\underline{-35y+35y}=-147+115} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4y=-28 \\-4x=-32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-28}{4}=-7 \\x=\frac{-32}{-4}=8\end{matrix}\right.\\ \qquad V=\{(8,-7)\}\)
  7. \(\left\{\begin{matrix}-4y-10x=66\\3x+9y=-90\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x-4y=66\\3x+9y=-90\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x-4y=66& \color{red}{3.} & \color{blue}{9.} \\3x+9y=-90& \color{red}{10.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}-12y+90y=198-900} \\ \color{blue}{-90x+12x\underline{-36y+36y}=594-360} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}78y=-702 \\-78x=234\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-702}{78}=-9 \\x=\frac{234}{-78}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-9)\}\)
  8. \(\left\{\begin{matrix}-9x+7y=39\\-9y+2x=36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x+7y=39\\2x-9y=36\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+7y=39& \color{red}{2.} & \color{blue}{9.} \\2x-9y=36& \color{red}{9.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}+14y-81y=78+324} \\ \color{blue}{-81x+14x\underline{+63y-63y}=351+252} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-67y=402 \\-67x=603\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{402}{-67}=-6 \\x=\frac{603}{-67}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-6)\}\)
  9. \(\left\{\begin{matrix}-6x-10y=-68\\6x-4y=-44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-10y=-68& \color{red}{1.} & \color{blue}{2.} \\6x-4y=-44& \color{red}{1.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}-10y-4y=-68-44} \\ \color{blue}{-12x-30x\underline{-20y+20y}=-136+220} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-14y=-112 \\-42x=84\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-112}{-14}=8 \\x=\frac{84}{-42}=-2\end{matrix}\right.\\ \qquad V=\{(-2,8)\}\)
  10. \(\left\{\begin{matrix}-8x+2y=-44\\-3y-6x=-42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+2y=-44\\-6x-3y=-42\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+2y=-44& \color{red}{3.} & \color{blue}{3.} \\-6x-3y=-42& \color{red}{-4.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}+6y+12y=-132+168} \\ \color{blue}{-24x-12x\underline{+6y-6y}=-132-84} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}18y=36 \\-36x=-216\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{36}{18}=2 \\x=\frac{-216}{-36}=6\end{matrix}\right.\\ \qquad V=\{(6,2)\}\)
  11. \(\left\{\begin{matrix}4x-4y=4\\7y-2x=13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-4y=4\\-2x+7y=13\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x-4y=4& \color{red}{1.} & \color{blue}{7.} \\-2x+7y=13& \color{red}{2.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{4x-4x}-4y+14y=4+26} \\ \color{blue}{28x-8x\underline{-28y+28y}=28+52} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10y=30 \\20x=80\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{30}{10}=3 \\x=\frac{80}{20}=4\end{matrix}\right.\\ \qquad V=\{(4,3)\}\)
  12. \(\left\{\begin{matrix}10x-7y=-96\\8x-5y=-72\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-7y=-96& \color{red}{4.} & \color{blue}{5.} \\8x-5y=-72& \color{red}{-5.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}-28y+25y=-384+360} \\ \color{blue}{50x-56x\underline{-35y+35y}=-480+504} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3y=-24 \\-6x=24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-24}{-3}=8 \\x=\frac{24}{-6}=-4\end{matrix}\right.\\ \qquad V=\{(-4,8)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-02 01:42:23