Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}7x+4y=60\\-9x=5y-77\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}10x-3y=-59\\-8x=-9y+1\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}8y+9x=-89\\-9x+2y=-11\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}6y-7x=-15\\9x+9y=-81\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-9y=106-4x\\9x-10y=136\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-7x-10y=73\\3y-2x=-26\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}3x-3y=-15\\10y+6x=-78\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-3x-9y=21\\-10y-7x=38\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}3x-5y=25\\5x-9y=43\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-6x-4y=64\\8x+3y=-83\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}9y=-76+2x\\-3x-2y=10\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-6x+3y=63\\-6x-8y=52\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}7x+4y=60\\-9x=5y-77\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+4y=60\\-9x-5y=-77\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+4y=60& \color{red}{9.} & \color{blue}{5.} \\-9x-5y=-77& \color{red}{7.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{63x-63x}+36y-35y=540-539} \\ \color{blue}{35x-36x\underline{+20y-20y}=300-308} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=1 \\-x=-8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{1}{1}=1 \\x=\frac{-8}{-1}=8\end{matrix}\right.\\ \qquad V=\{(8,1)\}\)
  2. \(\left\{\begin{matrix}10x-3y=-59\\-8x=-9y+1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x-3y=-59\\-8x+9y=1\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-3y=-59& \color{red}{4.} & \color{blue}{3.} \\-8x+9y=1& \color{red}{5.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}-12y+45y=-236+5} \\ \color{blue}{30x-8x\underline{-9y+9y}=-177+1} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}33y=-231 \\22x=-176\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-231}{33}=-7 \\x=\frac{-176}{22}=-8\end{matrix}\right.\\ \qquad V=\{(-8,-7)\}\)
  3. \(\left\{\begin{matrix}8y+9x=-89\\-9x+2y=-11\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x+8y=-89\\-9x+2y=-11\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+8y=-89& \color{red}{1.} & \color{blue}{1.} \\-9x+2y=-11& \color{red}{1.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{9x-9x}+8y+2y=-89-11} \\ \color{blue}{9x+36x\underline{+8y-8y}=-89+44} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10y=-100 \\45x=-45\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-100}{10}=-10 \\x=\frac{-45}{45}=-1\end{matrix}\right.\\ \qquad V=\{(-1,-10)\}\)
  4. \(\left\{\begin{matrix}6y-7x=-15\\9x+9y=-81\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x+6y=-15\\9x+9y=-81\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x+6y=-15& \color{red}{9.} & \color{blue}{3.} \\9x+9y=-81& \color{red}{7.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-63x+63x}+54y+63y=-135-567} \\ \color{blue}{-21x-18x\underline{+18y-18y}=-45+162} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}117y=-702 \\-39x=117\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-702}{117}=-6 \\x=\frac{117}{-39}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-6)\}\)
  5. \(\left\{\begin{matrix}-9y=106-4x\\9x-10y=136\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-9y=106\\9x-10y=136\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x-9y=106& \color{red}{9.} & \color{blue}{10.} \\9x-10y=136& \color{red}{-4.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{36x-36x}-81y+40y=954-544} \\ \color{blue}{40x-81x\underline{-90y+90y}=1060-1224} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-41y=410 \\-41x=-164\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{410}{-41}=-10 \\x=\frac{-164}{-41}=4\end{matrix}\right.\\ \qquad V=\{(4,-10)\}\)
  6. \(\left\{\begin{matrix}-7x-10y=73\\3y-2x=-26\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-10y=73\\-2x+3y=-26\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-10y=73& \color{red}{2.} & \color{blue}{3.} \\-2x+3y=-26& \color{red}{-7.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-14x+14x}-20y-21y=146+182} \\ \color{blue}{-21x-20x\underline{-30y+30y}=219-260} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-41y=328 \\-41x=-41\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{328}{-41}=-8 \\x=\frac{-41}{-41}=1\end{matrix}\right.\\ \qquad V=\{(1,-8)\}\)
  7. \(\left\{\begin{matrix}3x-3y=-15\\10y+6x=-78\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-3y=-15\\6x+10y=-78\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-3y=-15& \color{red}{2.} & \color{blue}{10.} \\6x+10y=-78& \color{red}{-1.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}-6y-10y=-30+78} \\ \color{blue}{30x+18x\underline{-30y+30y}=-150-234} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-16y=48 \\48x=-384\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{48}{-16}=-3 \\x=\frac{-384}{48}=-8\end{matrix}\right.\\ \qquad V=\{(-8,-3)\}\)
  8. \(\left\{\begin{matrix}-3x-9y=21\\-10y-7x=38\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x-9y=21\\-7x-10y=38\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x-9y=21& \color{red}{7.} & \color{blue}{10.} \\-7x-10y=38& \color{red}{-3.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-21x+21x}-63y+30y=147-114} \\ \color{blue}{-30x+63x\underline{-90y+90y}=210-342} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-33y=33 \\33x=-132\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{33}{-33}=-1 \\x=\frac{-132}{33}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-1)\}\)
  9. \(\left\{\begin{matrix}3x-5y=25\\5x-9y=43\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-5y=25& \color{red}{5.} & \color{blue}{9.} \\5x-9y=43& \color{red}{-3.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{15x-15x}-25y+27y=125-129} \\ \color{blue}{27x-25x\underline{-45y+45y}=225-215} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2y=-4 \\2x=10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-4}{2}=-2 \\x=\frac{10}{2}=5\end{matrix}\right.\\ \qquad V=\{(5,-2)\}\)
  10. \(\left\{\begin{matrix}-6x-4y=64\\8x+3y=-83\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-4y=64& \color{red}{4.} & \color{blue}{3.} \\8x+3y=-83& \color{red}{3.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}-16y+9y=256-249} \\ \color{blue}{-18x+32x\underline{-12y+12y}=192-332} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7y=7 \\14x=-140\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{7}{-7}=-1 \\x=\frac{-140}{14}=-10\end{matrix}\right.\\ \qquad V=\{(-10,-1)\}\)
  11. \(\left\{\begin{matrix}9y=-76+2x\\-3x-2y=10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+9y=-76\\-3x-2y=10\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+9y=-76& \color{red}{3.} & \color{blue}{2.} \\-3x-2y=10& \color{red}{-2.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+27y+4y=-228-20} \\ \color{blue}{-4x-27x\underline{+18y-18y}=-152+90} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}31y=-248 \\-31x=-62\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-248}{31}=-8 \\x=\frac{-62}{-31}=2\end{matrix}\right.\\ \qquad V=\{(2,-8)\}\)
  12. \(\left\{\begin{matrix}-6x+3y=63\\-6x-8y=52\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+3y=63& \color{red}{1.} & \color{blue}{8.} \\-6x-8y=52& \color{red}{-1.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+3y+8y=63-52} \\ \color{blue}{-48x-18x\underline{+24y-24y}=504+156} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}11y=11 \\-66x=660\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{11}{11}=1 \\x=\frac{660}{-66}=-10\end{matrix}\right.\\ \qquad V=\{(-10,1)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2022-08-18 12:38:25