Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}3x+2y=-14\\-5y-9x=41\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}5x-4y=-14\\2x=10y+28\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}-3x+3y=21\\-9x+8y=64\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-10y=-62-2x\\-3x+8y=51\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}2x-9y=15\\-5x=-10y-25\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-10x-4y=-124\\-6x+10y=0\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-5y-4x=-11\\6x+7y=17\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-3y=-88+7x\\6x-4y=36\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}8y=84-10x\\5x-3y=-14\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-8x+3y=-45\\4x=-8y-44\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}-4x+6y=-48\\-8y+5x=62\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}4y+6x=76\\-8x-9y=-116\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}3x+2y=-14\\-5y-9x=41\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+2y=-14\\-9x-5y=41\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+2y=-14& \color{red}{3.} & \color{blue}{5.} \\-9x-5y=41& \color{red}{1.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{9x-9x}+6y-5y=-42+41} \\ \color{blue}{15x-18x\underline{+10y-10y}=-70+82} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-1 \\-3x=12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-1}{1}=-1 \\x=\frac{12}{-3}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-1)\}\)
  2. \(\left\{\begin{matrix}5x-4y=-14\\2x=10y+28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-4y=-14\\2x-10y=28\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-4y=-14& \color{red}{2.} & \color{blue}{5.} \\2x-10y=28& \color{red}{-5.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-8y+50y=-28-140} \\ \color{blue}{25x-4x\underline{-20y+20y}=-70-56} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}42y=-168 \\21x=-126\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-168}{42}=-4 \\x=\frac{-126}{21}=-6\end{matrix}\right.\\ \qquad V=\{(-6,-4)\}\)
  3. \(\left\{\begin{matrix}-3x+3y=21\\-9x+8y=64\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+3y=21& \color{red}{3.} & \color{blue}{8.} \\-9x+8y=64& \color{red}{-1.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-9x+9x}+9y-8y=63-64} \\ \color{blue}{-24x+27x\underline{+24y-24y}=168-192} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-1 \\3x=-24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-1}{1}=-1 \\x=\frac{-24}{3}=-8\end{matrix}\right.\\ \qquad V=\{(-8,-1)\}\)
  4. \(\left\{\begin{matrix}-10y=-62-2x\\-3x+8y=51\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x-10y=-62\\-3x+8y=51\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x-10y=-62& \color{red}{3.} & \color{blue}{4.} \\-3x+8y=51& \color{red}{2.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}-30y+16y=-186+102} \\ \color{blue}{8x-15x\underline{-40y+40y}=-248+255} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-14y=-84 \\-7x=7\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-84}{-14}=6 \\x=\frac{7}{-7}=-1\end{matrix}\right.\\ \qquad V=\{(-1,6)\}\)
  5. \(\left\{\begin{matrix}2x-9y=15\\-5x=-10y-25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x-9y=15\\-5x+10y=-25\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x-9y=15& \color{red}{5.} & \color{blue}{10.} \\-5x+10y=-25& \color{red}{2.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-45y+20y=75-50} \\ \color{blue}{20x-45x\underline{-90y+90y}=150-225} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-25y=25 \\-25x=-75\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{25}{-25}=-1 \\x=\frac{-75}{-25}=3\end{matrix}\right.\\ \qquad V=\{(3,-1)\}\)
  6. \(\left\{\begin{matrix}-10x-4y=-124\\-6x+10y=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x-4y=-124& \color{red}{3.} & \color{blue}{5.} \\-6x+10y=0& \color{red}{-5.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}-12y-50y=-372+0} \\ \color{blue}{-50x-12x\underline{-20y+20y}=-620+0} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-62y=-372 \\-62x=-620\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-372}{-62}=6 \\x=\frac{-620}{-62}=10\end{matrix}\right.\\ \qquad V=\{(10,6)\}\)
  7. \(\left\{\begin{matrix}-5y-4x=-11\\6x+7y=17\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-5y=-11\\6x+7y=17\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x-5y=-11& \color{red}{3.} & \color{blue}{7.} \\6x+7y=17& \color{red}{2.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-12x+12x}-15y+14y=-33+34} \\ \color{blue}{-28x+30x\underline{-35y+35y}=-77+85} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-y=1 \\2x=8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{1}{-1}=-1 \\x=\frac{8}{2}=4\end{matrix}\right.\\ \qquad V=\{(4,-1)\}\)
  8. \(\left\{\begin{matrix}-3y=-88+7x\\6x-4y=36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-3y=-88\\6x-4y=36\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-3y=-88& \color{red}{6.} & \color{blue}{4.} \\6x-4y=36& \color{red}{7.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-42x+42x}-18y-28y=-528+252} \\ \color{blue}{-28x-18x\underline{-12y+12y}=-352-108} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-46y=-276 \\-46x=-460\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-276}{-46}=6 \\x=\frac{-460}{-46}=10\end{matrix}\right.\\ \qquad V=\{(10,6)\}\)
  9. \(\left\{\begin{matrix}8y=84-10x\\5x-3y=-14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x+8y=84\\5x-3y=-14\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x+8y=84& \color{red}{1.} & \color{blue}{3.} \\5x-3y=-14& \color{red}{-2.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}+8y+6y=84+28} \\ \color{blue}{30x+40x\underline{+24y-24y}=252-112} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}14y=112 \\70x=140\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{112}{14}=8 \\x=\frac{140}{70}=2\end{matrix}\right.\\ \qquad V=\{(2,8)\}\)
  10. \(\left\{\begin{matrix}-8x+3y=-45\\4x=-8y-44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+3y=-45\\4x+8y=-44\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+3y=-45& \color{red}{1.} & \color{blue}{8.} \\4x+8y=-44& \color{red}{2.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}+3y+16y=-45-88} \\ \color{blue}{-64x-12x\underline{+24y-24y}=-360+132} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}19y=-133 \\-76x=-228\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-133}{19}=-7 \\x=\frac{-228}{-76}=3\end{matrix}\right.\\ \qquad V=\{(3,-7)\}\)
  11. \(\left\{\begin{matrix}-4x+6y=-48\\-8y+5x=62\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+6y=-48\\5x-8y=62\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x+6y=-48& \color{red}{5.} & \color{blue}{4.} \\5x-8y=62& \color{red}{4.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-20x+20x}+30y-32y=-240+248} \\ \color{blue}{-16x+15x\underline{+24y-24y}=-192+186} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2y=8 \\-x=-6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{8}{-2}=-4 \\x=\frac{-6}{-1}=6\end{matrix}\right.\\ \qquad V=\{(6,-4)\}\)
  12. \(\left\{\begin{matrix}4y+6x=76\\-8x-9y=-116\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+4y=76\\-8x-9y=-116\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x+4y=76& \color{red}{4.} & \color{blue}{9.} \\-8x-9y=-116& \color{red}{3.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{24x-24x}+16y-27y=304-348} \\ \color{blue}{54x-32x\underline{+36y-36y}=684-464} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-11y=-44 \\22x=220\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-44}{-11}=4 \\x=\frac{220}{22}=10\end{matrix}\right.\\ \qquad V=\{(10,4)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-02 17:15:25