Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}3x+10y=-121\\-6x=2y+62\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}-6y=-16-5x\\2x+3y=-1\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}6x+3y=18\\-9y-9x=-63\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-2x+7y=1\\9x=8y-28\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}3x-8y=-59\\10y-4x=74\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}10x-3y=3\\5y-3x=36\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}2x-8y=-46\\-7x=-5y-23\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}2x+8y=-42\\7y-5x=-30\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}2x-5y=23\\4x-2y=-10\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-2x+8y=50\\-7x+9y=23\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}2y=24+10x\\-9x-4y=39\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-9x+5y=31\\-8x=3y+102\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}3x+10y=-121\\-6x=2y+62\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+10y=-121\\-6x-2y=62\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+10y=-121& \color{red}{2.} & \color{blue}{1.} \\-6x-2y=62& \color{red}{1.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}+20y-2y=-242+62} \\ \color{blue}{3x-30x\underline{+10y-10y}=-121+310} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}18y=-180 \\-27x=189\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-180}{18}=-10 \\x=\frac{189}{-27}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-10)\}\)
  2. \(\left\{\begin{matrix}-6y=-16-5x\\2x+3y=-1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-6y=-16\\2x+3y=-1\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-6y=-16& \color{red}{2.} & \color{blue}{1.} \\2x+3y=-1& \color{red}{-5.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-12y-15y=-32+5} \\ \color{blue}{5x+4x\underline{-6y+6y}=-16-2} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-27y=-27 \\9x=-18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-27}{-27}=1 \\x=\frac{-18}{9}=-2\end{matrix}\right.\\ \qquad V=\{(-2,1)\}\)
  3. \(\left\{\begin{matrix}6x+3y=18\\-9y-9x=-63\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+3y=18\\-9x-9y=-63\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x+3y=18& \color{red}{3.} & \color{blue}{3.} \\-9x-9y=-63& \color{red}{2.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{18x-18x}+9y-18y=54-126} \\ \color{blue}{18x-9x\underline{+9y-9y}=54-63} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9y=-72 \\9x=-9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-72}{-9}=8 \\x=\frac{-9}{9}=-1\end{matrix}\right.\\ \qquad V=\{(-1,8)\}\)
  4. \(\left\{\begin{matrix}-2x+7y=1\\9x=8y-28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+7y=1\\9x-8y=-28\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+7y=1& \color{red}{9.} & \color{blue}{8.} \\9x-8y=-28& \color{red}{2.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}+63y-16y=9-56} \\ \color{blue}{-16x+63x\underline{+56y-56y}=8-196} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}47y=-47 \\47x=-188\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-47}{47}=-1 \\x=\frac{-188}{47}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-1)\}\)
  5. \(\left\{\begin{matrix}3x-8y=-59\\10y-4x=74\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-8y=-59\\-4x+10y=74\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-8y=-59& \color{red}{4.} & \color{blue}{5.} \\-4x+10y=74& \color{red}{3.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{12x-12x}-32y+30y=-236+222} \\ \color{blue}{15x-16x\underline{-40y+40y}=-295+296} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2y=-14 \\-x=1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-14}{-2}=7 \\x=\frac{1}{-1}=-1\end{matrix}\right.\\ \qquad V=\{(-1,7)\}\)
  6. \(\left\{\begin{matrix}10x-3y=3\\5y-3x=36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x-3y=3\\-3x+5y=36\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-3y=3& \color{red}{3.} & \color{blue}{5.} \\-3x+5y=36& \color{red}{10.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}-9y+50y=9+360} \\ \color{blue}{50x-9x\underline{-15y+15y}=15+108} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}41y=369 \\41x=123\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{369}{41}=9 \\x=\frac{123}{41}=3\end{matrix}\right.\\ \qquad V=\{(3,9)\}\)
  7. \(\left\{\begin{matrix}2x-8y=-46\\-7x=-5y-23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x-8y=-46\\-7x+5y=-23\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x-8y=-46& \color{red}{7.} & \color{blue}{5.} \\-7x+5y=-23& \color{red}{2.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{14x-14x}-56y+10y=-322-46} \\ \color{blue}{10x-56x\underline{-40y+40y}=-230-184} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-46y=-368 \\-46x=-414\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-368}{-46}=8 \\x=\frac{-414}{-46}=9\end{matrix}\right.\\ \qquad V=\{(9,8)\}\)
  8. \(\left\{\begin{matrix}2x+8y=-42\\7y-5x=-30\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+8y=-42\\-5x+7y=-30\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+8y=-42& \color{red}{5.} & \color{blue}{7.} \\-5x+7y=-30& \color{red}{2.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}+40y+14y=-210-60} \\ \color{blue}{14x+40x\underline{+56y-56y}=-294+240} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}54y=-270 \\54x=-54\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-270}{54}=-5 \\x=\frac{-54}{54}=-1\end{matrix}\right.\\ \qquad V=\{(-1,-5)\}\)
  9. \(\left\{\begin{matrix}2x-5y=23\\4x-2y=-10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x-5y=23& \color{red}{2.} & \color{blue}{2.} \\4x-2y=-10& \color{red}{-1.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{4x-4x}-10y+2y=46+10} \\ \color{blue}{4x-20x\underline{-10y+10y}=46+50} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8y=56 \\-16x=96\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{56}{-8}=-7 \\x=\frac{96}{-16}=-6\end{matrix}\right.\\ \qquad V=\{(-6,-7)\}\)
  10. \(\left\{\begin{matrix}-2x+8y=50\\-7x+9y=23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+8y=50& \color{red}{7.} & \color{blue}{9.} \\-7x+9y=23& \color{red}{-2.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-14x+14x}+56y-18y=350-46} \\ \color{blue}{-18x+56x\underline{+72y-72y}=450-184} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}38y=304 \\38x=266\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{304}{38}=8 \\x=\frac{266}{38}=7\end{matrix}\right.\\ \qquad V=\{(7,8)\}\)
  11. \(\left\{\begin{matrix}2y=24+10x\\-9x-4y=39\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x+2y=24\\-9x-4y=39\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x+2y=24& \color{red}{9.} & \color{blue}{2.} \\-9x-4y=39& \color{red}{-10.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-90x+90x}+18y+40y=216-390} \\ \color{blue}{-20x-9x\underline{+4y-4y}=48+39} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}58y=-174 \\-29x=87\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-174}{58}=-3 \\x=\frac{87}{-29}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-3)\}\)
  12. \(\left\{\begin{matrix}-9x+5y=31\\-8x=3y+102\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x+5y=31\\-8x-3y=102\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+5y=31& \color{red}{8.} & \color{blue}{3.} \\-8x-3y=102& \color{red}{-9.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-72x+72x}+40y+27y=248-918} \\ \color{blue}{-27x-40x\underline{+15y-15y}=93+510} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}67y=-670 \\-67x=603\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-670}{67}=-10 \\x=\frac{603}{-67}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-10)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-04-02 04:44:50