Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}-9y=48+4x\\10x+7y=4\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}-7x-6y=4\\-7x=-3y-86\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}-7x-4y=39\\2x-5y=-48\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}6x+10y=14\\4x=9y-22\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}2y=-16+4x\\-9x+10y=-3\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-6x+4y=60\\-3x=10y-6\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}4y-8x=-56\\-3x+10y=-106\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-8x+5y=41\\-2x=-8y-10\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}2x+8y=38\\-7y-4x=-40\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-5y-7x=-54\\7x-9y=40\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}4x+7y=-103\\9x=-8y-162\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-2x+9y=-20\\5y-8x=44\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}-9y=48+4x\\10x+7y=4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-9y=48\\10x+7y=4\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x-9y=48& \color{red}{5.} & \color{blue}{7.} \\10x+7y=4& \color{red}{2.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-20x+20x}-45y+14y=240+8} \\ \color{blue}{-28x+90x\underline{-63y+63y}=336+36} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-31y=248 \\62x=372\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{248}{-31}=-8 \\x=\frac{372}{62}=6\end{matrix}\right.\\ \qquad V=\{(6,-8)\}\)
  2. \(\left\{\begin{matrix}-7x-6y=4\\-7x=-3y-86\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-6y=4\\-7x+3y=-86\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-6y=4& \color{red}{1.} & \color{blue}{1.} \\-7x+3y=-86& \color{red}{-1.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-7x+7x}-6y-3y=4+86} \\ \color{blue}{-7x-14x\underline{-6y+6y}=4-172} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9y=90 \\-21x=-168\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{90}{-9}=-10 \\x=\frac{-168}{-21}=8\end{matrix}\right.\\ \qquad V=\{(8,-10)\}\)
  3. \(\left\{\begin{matrix}-7x-4y=39\\2x-5y=-48\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-4y=39& \color{red}{2.} & \color{blue}{5.} \\2x-5y=-48& \color{red}{7.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-14x+14x}-8y-35y=78-336} \\ \color{blue}{-35x-8x\underline{-20y+20y}=195+192} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-43y=-258 \\-43x=387\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-258}{-43}=6 \\x=\frac{387}{-43}=-9\end{matrix}\right.\\ \qquad V=\{(-9,6)\}\)
  4. \(\left\{\begin{matrix}6x+10y=14\\4x=9y-22\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+10y=14\\4x-9y=-22\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x+10y=14& \color{red}{2.} & \color{blue}{9.} \\4x-9y=-22& \color{red}{-3.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{12x-12x}+20y+27y=28+66} \\ \color{blue}{54x+40x\underline{+90y-90y}=126-220} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}47y=94 \\94x=-94\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{94}{47}=2 \\x=\frac{-94}{94}=-1\end{matrix}\right.\\ \qquad V=\{(-1,2)\}\)
  5. \(\left\{\begin{matrix}2y=-16+4x\\-9x+10y=-3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+2y=-16\\-9x+10y=-3\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x+2y=-16& \color{red}{9.} & \color{blue}{5.} \\-9x+10y=-3& \color{red}{-4.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-36x+36x}+18y-40y=-144+12} \\ \color{blue}{-20x+9x\underline{+10y-10y}=-80+3} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-22y=-132 \\-11x=-77\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-132}{-22}=6 \\x=\frac{-77}{-11}=7\end{matrix}\right.\\ \qquad V=\{(7,6)\}\)
  6. \(\left\{\begin{matrix}-6x+4y=60\\-3x=10y-6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+4y=60\\-3x-10y=-6\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+4y=60& \color{red}{1.} & \color{blue}{5.} \\-3x-10y=-6& \color{red}{-2.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+4y+20y=60+12} \\ \color{blue}{-30x-6x\underline{+20y-20y}=300-12} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}24y=72 \\-36x=288\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{72}{24}=3 \\x=\frac{288}{-36}=-8\end{matrix}\right.\\ \qquad V=\{(-8,3)\}\)
  7. \(\left\{\begin{matrix}4y-8x=-56\\-3x+10y=-106\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+4y=-56\\-3x+10y=-106\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+4y=-56& \color{red}{3.} & \color{blue}{5.} \\-3x+10y=-106& \color{red}{-8.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}+12y-80y=-168+848} \\ \color{blue}{-40x+6x\underline{+20y-20y}=-280+212} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-68y=680 \\-34x=-68\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{680}{-68}=-10 \\x=\frac{-68}{-34}=2\end{matrix}\right.\\ \qquad V=\{(2,-10)\}\)
  8. \(\left\{\begin{matrix}-8x+5y=41\\-2x=-8y-10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+5y=41\\-2x+8y=-10\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+5y=41& \color{red}{1.} & \color{blue}{8.} \\-2x+8y=-10& \color{red}{-4.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}+5y-32y=41+40} \\ \color{blue}{-64x+10x\underline{+40y-40y}=328+50} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-27y=81 \\-54x=378\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{81}{-27}=-3 \\x=\frac{378}{-54}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-3)\}\)
  9. \(\left\{\begin{matrix}2x+8y=38\\-7y-4x=-40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+8y=38\\-4x-7y=-40\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+8y=38& \color{red}{2.} & \color{blue}{7.} \\-4x-7y=-40& \color{red}{1.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{4x-4x}+16y-7y=76-40} \\ \color{blue}{14x-32x\underline{+56y-56y}=266-320} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9y=36 \\-18x=-54\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{36}{9}=4 \\x=\frac{-54}{-18}=3\end{matrix}\right.\\ \qquad V=\{(3,4)\}\)
  10. \(\left\{\begin{matrix}-5y-7x=-54\\7x-9y=40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-5y=-54\\7x-9y=40\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-5y=-54& \color{red}{1.} & \color{blue}{9.} \\7x-9y=40& \color{red}{1.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-7x+7x}-5y-9y=-54+40} \\ \color{blue}{-63x-35x\underline{-45y+45y}=-486-200} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-14y=-14 \\-98x=-686\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-14}{-14}=1 \\x=\frac{-686}{-98}=7\end{matrix}\right.\\ \qquad V=\{(7,1)\}\)
  11. \(\left\{\begin{matrix}4x+7y=-103\\9x=-8y-162\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+7y=-103\\9x+8y=-162\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+7y=-103& \color{red}{9.} & \color{blue}{8.} \\9x+8y=-162& \color{red}{-4.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{36x-36x}+63y-32y=-927+648} \\ \color{blue}{32x-63x\underline{+56y-56y}=-824+1134} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}31y=-279 \\-31x=310\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-279}{31}=-9 \\x=\frac{310}{-31}=-10\end{matrix}\right.\\ \qquad V=\{(-10,-9)\}\)
  12. \(\left\{\begin{matrix}-2x+9y=-20\\5y-8x=44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+9y=-20\\-8x+5y=44\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+9y=-20& \color{red}{4.} & \color{blue}{5.} \\-8x+5y=44& \color{red}{-1.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}+36y-5y=-80-44} \\ \color{blue}{-10x+72x\underline{+45y-45y}=-100-396} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}31y=-124 \\62x=-496\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-124}{31}=-4 \\x=\frac{-496}{62}=-8\end{matrix}\right.\\ \qquad V=\{(-8,-4)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-07 13:43:03