Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}-5x+10y=85\\-10x=-2y+8\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}10x-4y=22\\-6y-9x=57\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}-7y=-133-7x\\-6x+5y=104\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}3y=106-10x\\-10x-8y=-116\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}9x+9y=72\\-9x-4y=-77\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-2y-8x=-10\\9x+5y=-8\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-9y=27+2x\\5x+5y=20\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}6x-4y=72\\6x-3y=63\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}-5y=28+4x\\8x-3y=48\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}7x+7y=0\\-7x=-2y-63\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}9y=14-4x\\8x-2y=-92\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}3y+2x=-4\\-10x+9y=68\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}-5x+10y=85\\-10x=-2y+8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+10y=85\\-10x+2y=8\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x+10y=85& \color{red}{2.} & \color{blue}{1.} \\-10x+2y=8& \color{red}{-1.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}+20y-2y=170-8} \\ \color{blue}{-5x+50x\underline{+10y-10y}=85-40} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}18y=162 \\45x=45\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{162}{18}=9 \\x=\frac{45}{45}=1\end{matrix}\right.\\ \qquad V=\{(1,9)\}\)
  2. \(\left\{\begin{matrix}10x-4y=22\\-6y-9x=57\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x-4y=22\\-9x-6y=57\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-4y=22& \color{red}{9.} & \color{blue}{3.} \\-9x-6y=57& \color{red}{10.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{90x-90x}-36y-60y=198+570} \\ \color{blue}{30x+18x\underline{-12y+12y}=66-114} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-96y=768 \\48x=-48\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{768}{-96}=-8 \\x=\frac{-48}{48}=-1\end{matrix}\right.\\ \qquad V=\{(-1,-8)\}\)
  3. \(\left\{\begin{matrix}-7y=-133-7x\\-6x+5y=104\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x-7y=-133\\-6x+5y=104\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-7y=-133& \color{red}{6.} & \color{blue}{5.} \\-6x+5y=104& \color{red}{7.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{42x-42x}-42y+35y=-798+728} \\ \color{blue}{35x-42x\underline{-35y+35y}=-665+728} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7y=-70 \\-7x=63\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-70}{-7}=10 \\x=\frac{63}{-7}=-9\end{matrix}\right.\\ \qquad V=\{(-9,10)\}\)
  4. \(\left\{\begin{matrix}3y=106-10x\\-10x-8y=-116\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x+3y=106\\-10x-8y=-116\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x+3y=106& \color{red}{1.} & \color{blue}{8.} \\-10x-8y=-116& \color{red}{1.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}+3y-8y=106-116} \\ \color{blue}{80x-30x\underline{+24y-24y}=848-348} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5y=-10 \\50x=500\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-10}{-5}=2 \\x=\frac{500}{50}=10\end{matrix}\right.\\ \qquad V=\{(10,2)\}\)
  5. \(\left\{\begin{matrix}9x+9y=72\\-9x-4y=-77\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+9y=72& \color{red}{1.} & \color{blue}{4.} \\-9x-4y=-77& \color{red}{1.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{9x-9x}+9y-4y=72-77} \\ \color{blue}{36x-81x\underline{+36y-36y}=288-693} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5y=-5 \\-45x=-405\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-5}{5}=-1 \\x=\frac{-405}{-45}=9\end{matrix}\right.\\ \qquad V=\{(9,-1)\}\)
  6. \(\left\{\begin{matrix}-2y-8x=-10\\9x+5y=-8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-2y=-10\\9x+5y=-8\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-2y=-10& \color{red}{9.} & \color{blue}{5.} \\9x+5y=-8& \color{red}{8.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-72x+72x}-18y+40y=-90-64} \\ \color{blue}{-40x+18x\underline{-10y+10y}=-50-16} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}22y=-154 \\-22x=-66\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-154}{22}=-7 \\x=\frac{-66}{-22}=3\end{matrix}\right.\\ \qquad V=\{(3,-7)\}\)
  7. \(\left\{\begin{matrix}-9y=27+2x\\5x+5y=20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-9y=27\\5x+5y=20\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x-9y=27& \color{red}{5.} & \color{blue}{5.} \\5x+5y=20& \color{red}{2.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}-45y+10y=135+40} \\ \color{blue}{-10x+45x\underline{-45y+45y}=135+180} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-35y=175 \\35x=315\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{175}{-35}=-5 \\x=\frac{315}{35}=9\end{matrix}\right.\\ \qquad V=\{(9,-5)\}\)
  8. \(\left\{\begin{matrix}6x-4y=72\\6x-3y=63\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-4y=72& \color{red}{1.} & \color{blue}{3.} \\6x-3y=63& \color{red}{-1.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}-4y+3y=72-63} \\ \color{blue}{18x-24x\underline{-12y+12y}=216-252} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-y=9 \\-6x=-36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{9}{-1}=-9 \\x=\frac{-36}{-6}=6\end{matrix}\right.\\ \qquad V=\{(6,-9)\}\)
  9. \(\left\{\begin{matrix}-5y=28+4x\\8x-3y=48\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-5y=28\\8x-3y=48\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x-5y=28& \color{red}{2.} & \color{blue}{3.} \\8x-3y=48& \color{red}{1.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}-10y-3y=56+48} \\ \color{blue}{-12x-40x\underline{-15y+15y}=84-240} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-13y=104 \\-52x=-156\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{104}{-13}=-8 \\x=\frac{-156}{-52}=3\end{matrix}\right.\\ \qquad V=\{(3,-8)\}\)
  10. \(\left\{\begin{matrix}7x+7y=0\\-7x=-2y-63\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+7y=0\\-7x+2y=-63\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+7y=0& \color{red}{1.} & \color{blue}{2.} \\-7x+2y=-63& \color{red}{1.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{7x-7x}+7y+2y=0-63} \\ \color{blue}{14x+49x\underline{+14y-14y}=0+441} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9y=-63 \\63x=441\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-63}{9}=-7 \\x=\frac{441}{63}=7\end{matrix}\right.\\ \qquad V=\{(7,-7)\}\)
  11. \(\left\{\begin{matrix}9y=14-4x\\8x-2y=-92\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+9y=14\\8x-2y=-92\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+9y=14& \color{red}{2.} & \color{blue}{2.} \\8x-2y=-92& \color{red}{-1.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}+18y+2y=28+92} \\ \color{blue}{8x+72x\underline{+18y-18y}=28-828} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}20y=120 \\80x=-800\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{120}{20}=6 \\x=\frac{-800}{80}=-10\end{matrix}\right.\\ \qquad V=\{(-10,6)\}\)
  12. \(\left\{\begin{matrix}3y+2x=-4\\-10x+9y=68\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+3y=-4\\-10x+9y=68\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+3y=-4& \color{red}{5.} & \color{blue}{3.} \\-10x+9y=68& \color{red}{1.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}+15y+9y=-20+68} \\ \color{blue}{6x+10x\underline{+9y-9y}=-12-68} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}24y=48 \\16x=-80\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{48}{24}=2 \\x=\frac{-80}{16}=-5\end{matrix}\right.\\ \qquad V=\{(-5,2)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-05-30 04:24:12