Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}3y-2x=1\\-3x-7y=13\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}-9y+7x=-22\\4x+3y=-37\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}-10y+6x=-130\\-5x+8y=106\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-2x+8y=36\\-4x=-2y+16\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-8x-2y=92\\-6y-2x=78\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}4y=-4+6x\\-9x+8y=-20\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-4y=-34+10x\\6x+5y=10\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}3y=-23+5x\\-3x+6y=-18\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}5x-10y=35\\-4x+9y=-33\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-7x-3y=-23\\-8x-7y=-12\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}4x+10y=-12\\-3y-7x=-37\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-4x+9y=3\\7x=-4y-25\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}3y-2x=1\\-3x-7y=13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+3y=1\\-3x-7y=13\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+3y=1& \color{red}{3.} & \color{blue}{7.} \\-3x-7y=13& \color{red}{-2.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+9y+14y=3-26} \\ \color{blue}{-14x-9x\underline{+21y-21y}=7+39} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}23y=-23 \\-23x=46\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-23}{23}=-1 \\x=\frac{46}{-23}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-1)\}\)
  2. \(\left\{\begin{matrix}-9y+7x=-22\\4x+3y=-37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x-9y=-22\\4x+3y=-37\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-9y=-22& \color{red}{4.} & \color{blue}{1.} \\4x+3y=-37& \color{red}{-7.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{28x-28x}-36y-21y=-88+259} \\ \color{blue}{7x+12x\underline{-9y+9y}=-22-111} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-57y=171 \\19x=-133\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{171}{-57}=-3 \\x=\frac{-133}{19}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-3)\}\)
  3. \(\left\{\begin{matrix}-10y+6x=-130\\-5x+8y=106\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x-10y=-130\\-5x+8y=106\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-10y=-130& \color{red}{5.} & \color{blue}{4.} \\-5x+8y=106& \color{red}{6.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}-50y+48y=-650+636} \\ \color{blue}{24x-25x\underline{-40y+40y}=-520+530} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2y=-14 \\-x=10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-14}{-2}=7 \\x=\frac{10}{-1}=-10\end{matrix}\right.\\ \qquad V=\{(-10,7)\}\)
  4. \(\left\{\begin{matrix}-2x+8y=36\\-4x=-2y+16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+8y=36\\-4x+2y=16\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+8y=36& \color{red}{2.} & \color{blue}{1.} \\-4x+2y=16& \color{red}{-1.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-4x+4x}+16y-2y=72-16} \\ \color{blue}{-2x+16x\underline{+8y-8y}=36-64} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}14y=56 \\14x=-28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{56}{14}=4 \\x=\frac{-28}{14}=-2\end{matrix}\right.\\ \qquad V=\{(-2,4)\}\)
  5. \(\left\{\begin{matrix}-8x-2y=92\\-6y-2x=78\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-2y=92\\-2x-6y=78\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-2y=92& \color{red}{1.} & \color{blue}{3.} \\-2x-6y=78& \color{red}{-4.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}-2y+24y=92-312} \\ \color{blue}{-24x+2x\underline{-6y+6y}=276-78} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}22y=-220 \\-22x=198\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-220}{22}=-10 \\x=\frac{198}{-22}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-10)\}\)
  6. \(\left\{\begin{matrix}4y=-4+6x\\-9x+8y=-20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+4y=-4\\-9x+8y=-20\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+4y=-4& \color{red}{3.} & \color{blue}{2.} \\-9x+8y=-20& \color{red}{-2.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}+12y-16y=-12+40} \\ \color{blue}{-12x+9x\underline{+8y-8y}=-8+20} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4y=28 \\-3x=12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{28}{-4}=-7 \\x=\frac{12}{-3}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-7)\}\)
  7. \(\left\{\begin{matrix}-4y=-34+10x\\6x+5y=10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x-4y=-34\\6x+5y=10\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x-4y=-34& \color{red}{3.} & \color{blue}{5.} \\6x+5y=10& \color{red}{5.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}-12y+25y=-102+50} \\ \color{blue}{-50x+24x\underline{-20y+20y}=-170+40} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}13y=-52 \\-26x=-130\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-52}{13}=-4 \\x=\frac{-130}{-26}=5\end{matrix}\right.\\ \qquad V=\{(5,-4)\}\)
  8. \(\left\{\begin{matrix}3y=-23+5x\\-3x+6y=-18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+3y=-23\\-3x+6y=-18\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x+3y=-23& \color{red}{3.} & \color{blue}{2.} \\-3x+6y=-18& \color{red}{-5.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-15x+15x}+9y-30y=-69+90} \\ \color{blue}{-10x+3x\underline{+6y-6y}=-46+18} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-21y=21 \\-7x=-28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{21}{-21}=-1 \\x=\frac{-28}{-7}=4\end{matrix}\right.\\ \qquad V=\{(4,-1)\}\)
  9. \(\left\{\begin{matrix}5x-10y=35\\-4x+9y=-33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-10y=35& \color{red}{4.} & \color{blue}{9.} \\-4x+9y=-33& \color{red}{5.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}-40y+45y=140-165} \\ \color{blue}{45x-40x\underline{-90y+90y}=315-330} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5y=-25 \\5x=-15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-25}{5}=-5 \\x=\frac{-15}{5}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-5)\}\)
  10. \(\left\{\begin{matrix}-7x-3y=-23\\-8x-7y=-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-3y=-23& \color{red}{8.} & \color{blue}{7.} \\-8x-7y=-12& \color{red}{-7.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-56x+56x}-24y+49y=-184+84} \\ \color{blue}{-49x+24x\underline{-21y+21y}=-161+36} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}25y=-100 \\-25x=-125\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-100}{25}=-4 \\x=\frac{-125}{-25}=5\end{matrix}\right.\\ \qquad V=\{(5,-4)\}\)
  11. \(\left\{\begin{matrix}4x+10y=-12\\-3y-7x=-37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+10y=-12\\-7x-3y=-37\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+10y=-12& \color{red}{7.} & \color{blue}{3.} \\-7x-3y=-37& \color{red}{4.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{28x-28x}+70y-12y=-84-148} \\ \color{blue}{12x-70x\underline{+30y-30y}=-36-370} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}58y=-232 \\-58x=-406\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-232}{58}=-4 \\x=\frac{-406}{-58}=7\end{matrix}\right.\\ \qquad V=\{(7,-4)\}\)
  12. \(\left\{\begin{matrix}-4x+9y=3\\7x=-4y-25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+9y=3\\7x+4y=-25\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x+9y=3& \color{red}{7.} & \color{blue}{4.} \\7x+4y=-25& \color{red}{4.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-28x+28x}+63y+16y=21-100} \\ \color{blue}{-16x-63x\underline{+36y-36y}=12+225} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}79y=-79 \\-79x=237\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-79}{79}=-1 \\x=\frac{237}{-79}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-1)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-03 14:37:26