Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}7y+5x=-31\\-2x-3y=13\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}6x-2y=-24\\8x-9y=25\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}5x+5y=40\\-9y-6x=-45\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-8x-10y=-170\\6y+5x=104\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}6y-2x=-38\\-7x+7y=-77\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-4y-6x=-18\\-4x+7y=-70\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-9y-10x=73\\-8x+7y=101\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}8x+7y=-80\\-8x=-10y-56\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}5x-2y=-43\\-8x=7y+28\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-6x-6y=-36\\-8x-5y=-42\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}-7y+9x=72\\4x-9y=85\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}4x+2y=-2\\-6y+10x=-82\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}7y+5x=-31\\-2x-3y=13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x+7y=-31\\-2x-3y=13\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x+7y=-31& \color{red}{2.} & \color{blue}{3.} \\-2x-3y=13& \color{red}{5.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}+14y-15y=-62+65} \\ \color{blue}{15x-14x\underline{+21y-21y}=-93+91} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-y=3 \\x=-2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{3}{-1}=-3 \\x=\frac{-2}{1}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-3)\}\)
  2. \(\left\{\begin{matrix}6x-2y=-24\\8x-9y=25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-2y=-24& \color{red}{4.} & \color{blue}{9.} \\8x-9y=25& \color{red}{-3.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{24x-24x}-8y+27y=-96-75} \\ \color{blue}{54x-16x\underline{-18y+18y}=-216-50} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}19y=-171 \\38x=-266\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-171}{19}=-9 \\x=\frac{-266}{38}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-9)\}\)
  3. \(\left\{\begin{matrix}5x+5y=40\\-9y-6x=-45\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x+5y=40\\-6x-9y=-45\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x+5y=40& \color{red}{6.} & \color{blue}{9.} \\-6x-9y=-45& \color{red}{5.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}+30y-45y=240-225} \\ \color{blue}{45x-30x\underline{+45y-45y}=360-225} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-15y=15 \\15x=135\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{15}{-15}=-1 \\x=\frac{135}{15}=9\end{matrix}\right.\\ \qquad V=\{(9,-1)\}\)
  4. \(\left\{\begin{matrix}-8x-10y=-170\\6y+5x=104\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-10y=-170\\5x+6y=104\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-10y=-170& \color{red}{5.} & \color{blue}{3.} \\5x+6y=104& \color{red}{8.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-40x+40x}-50y+48y=-850+832} \\ \color{blue}{-24x+25x\underline{-30y+30y}=-510+520} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2y=-18 \\x=10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-18}{-2}=9 \\x=\frac{10}{1}=10\end{matrix}\right.\\ \qquad V=\{(10,9)\}\)
  5. \(\left\{\begin{matrix}6y-2x=-38\\-7x+7y=-77\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+6y=-38\\-7x+7y=-77\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+6y=-38& \color{red}{7.} & \color{blue}{7.} \\-7x+7y=-77& \color{red}{-2.} & \color{blue}{-6.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-14x+14x}+42y-14y=-266+154} \\ \color{blue}{-14x+42x\underline{+42y-42y}=-266+462} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}28y=-112 \\28x=196\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-112}{28}=-4 \\x=\frac{196}{28}=7\end{matrix}\right.\\ \qquad V=\{(7,-4)\}\)
  6. \(\left\{\begin{matrix}-4y-6x=-18\\-4x+7y=-70\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x-4y=-18\\-4x+7y=-70\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-4y=-18& \color{red}{2.} & \color{blue}{7.} \\-4x+7y=-70& \color{red}{-3.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-12x+12x}-8y-21y=-36+210} \\ \color{blue}{-42x-16x\underline{-28y+28y}=-126-280} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-29y=174 \\-58x=-406\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{174}{-29}=-6 \\x=\frac{-406}{-58}=7\end{matrix}\right.\\ \qquad V=\{(7,-6)\}\)
  7. \(\left\{\begin{matrix}-9y-10x=73\\-8x+7y=101\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x-9y=73\\-8x+7y=101\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x-9y=73& \color{red}{4.} & \color{blue}{7.} \\-8x+7y=101& \color{red}{-5.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-40x+40x}-36y-35y=292-505} \\ \color{blue}{-70x-72x\underline{-63y+63y}=511+909} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-71y=-213 \\-142x=1420\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-213}{-71}=3 \\x=\frac{1420}{-142}=-10\end{matrix}\right.\\ \qquad V=\{(-10,3)\}\)
  8. \(\left\{\begin{matrix}8x+7y=-80\\-8x=-10y-56\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x+7y=-80\\-8x+10y=-56\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+7y=-80& \color{red}{1.} & \color{blue}{10.} \\-8x+10y=-56& \color{red}{1.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}+7y+10y=-80-56} \\ \color{blue}{80x+56x\underline{+70y-70y}=-800+392} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}17y=-136 \\136x=-408\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-136}{17}=-8 \\x=\frac{-408}{136}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-8)\}\)
  9. \(\left\{\begin{matrix}5x-2y=-43\\-8x=7y+28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-2y=-43\\-8x-7y=28\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-2y=-43& \color{red}{8.} & \color{blue}{7.} \\-8x-7y=28& \color{red}{5.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}-16y-35y=-344+140} \\ \color{blue}{35x+16x\underline{-14y+14y}=-301-56} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-51y=-204 \\51x=-357\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-204}{-51}=4 \\x=\frac{-357}{51}=-7\end{matrix}\right.\\ \qquad V=\{(-7,4)\}\)
  10. \(\left\{\begin{matrix}-6x-6y=-36\\-8x-5y=-42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-6y=-36& \color{red}{4.} & \color{blue}{5.} \\-8x-5y=-42& \color{red}{-3.} & \color{blue}{-6.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}-24y+15y=-144+126} \\ \color{blue}{-30x+48x\underline{-30y+30y}=-180+252} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9y=-18 \\18x=72\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-18}{-9}=2 \\x=\frac{72}{18}=4\end{matrix}\right.\\ \qquad V=\{(4,2)\}\)
  11. \(\left\{\begin{matrix}-7y+9x=72\\4x-9y=85\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x-7y=72\\4x-9y=85\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x-7y=72& \color{red}{4.} & \color{blue}{9.} \\4x-9y=85& \color{red}{-9.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{36x-36x}-28y+81y=288-765} \\ \color{blue}{81x-28x\underline{-63y+63y}=648-595} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}53y=-477 \\53x=53\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-477}{53}=-9 \\x=\frac{53}{53}=1\end{matrix}\right.\\ \qquad V=\{(1,-9)\}\)
  12. \(\left\{\begin{matrix}4x+2y=-2\\-6y+10x=-82\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+2y=-2\\10x-6y=-82\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+2y=-2& \color{red}{5.} & \color{blue}{3.} \\10x-6y=-82& \color{red}{-2.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}+10y+12y=-10+164} \\ \color{blue}{12x+10x\underline{+6y-6y}=-6-82} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}22y=154 \\22x=-88\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{154}{22}=7 \\x=\frac{-88}{22}=-4\end{matrix}\right.\\ \qquad V=\{(-4,7)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-04-02 10:53:04