Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}7y-7x=-105\\5x+2y=33\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}5x-5y=5\\3x=-2y+48\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}9y+3x=24\\-6x+4y=62\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-7x+10y=-13\\-8y+5x=5\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}3x-8y=2\\-4y+7x=-10\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}7x-8y=-66\\7x+9y=-15\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-2x-4y=30\\-7x-6y=25\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-5x-7y=16\\-3x+4y=26\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}-3x-7y=-13\\7x+5y=53\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}7x-5y=35\\10x=9y+37\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}6y=-36+6x\\10x+9y=-73\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-3y=-28-2x\\-2x-9y=-20\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}7y-7x=-105\\5x+2y=33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x+7y=-105\\5x+2y=33\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x+7y=-105& \color{red}{5.} & \color{blue}{2.} \\5x+2y=33& \color{red}{7.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-35x+35x}+35y+14y=-525+231} \\ \color{blue}{-14x-35x\underline{+14y-14y}=-210-231} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}49y=-294 \\-49x=-441\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-294}{49}=-6 \\x=\frac{-441}{-49}=9\end{matrix}\right.\\ \qquad V=\{(9,-6)\}\)
  2. \(\left\{\begin{matrix}5x-5y=5\\3x=-2y+48\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-5y=5\\3x+2y=48\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-5y=5& \color{red}{3.} & \color{blue}{2.} \\3x+2y=48& \color{red}{-5.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{15x-15x}-15y-10y=15-240} \\ \color{blue}{10x+15x\underline{-10y+10y}=10+240} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-25y=-225 \\25x=250\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-225}{-25}=9 \\x=\frac{250}{25}=10\end{matrix}\right.\\ \qquad V=\{(10,9)\}\)
  3. \(\left\{\begin{matrix}9y+3x=24\\-6x+4y=62\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+9y=24\\-6x+4y=62\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+9y=24& \color{red}{2.} & \color{blue}{4.} \\-6x+4y=62& \color{red}{1.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}+18y+4y=48+62} \\ \color{blue}{12x+54x\underline{+36y-36y}=96-558} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}22y=110 \\66x=-462\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{110}{22}=5 \\x=\frac{-462}{66}=-7\end{matrix}\right.\\ \qquad V=\{(-7,5)\}\)
  4. \(\left\{\begin{matrix}-7x+10y=-13\\-8y+5x=5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x+10y=-13\\5x-8y=5\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x+10y=-13& \color{red}{5.} & \color{blue}{4.} \\5x-8y=5& \color{red}{7.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-35x+35x}+50y-56y=-65+35} \\ \color{blue}{-28x+25x\underline{+40y-40y}=-52+25} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6y=-30 \\-3x=-27\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-30}{-6}=5 \\x=\frac{-27}{-3}=9\end{matrix}\right.\\ \qquad V=\{(9,5)\}\)
  5. \(\left\{\begin{matrix}3x-8y=2\\-4y+7x=-10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-8y=2\\7x-4y=-10\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-8y=2& \color{red}{7.} & \color{blue}{1.} \\7x-4y=-10& \color{red}{-3.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{21x-21x}-56y+12y=14+30} \\ \color{blue}{3x-14x\underline{-8y+8y}=2+20} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-44y=44 \\-11x=22\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{44}{-44}=-1 \\x=\frac{22}{-11}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-1)\}\)
  6. \(\left\{\begin{matrix}7x-8y=-66\\7x+9y=-15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-8y=-66& \color{red}{1.} & \color{blue}{9.} \\7x+9y=-15& \color{red}{-1.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{7x-7x}-8y-9y=-66+15} \\ \color{blue}{63x+56x\underline{-72y+72y}=-594-120} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-17y=-51 \\119x=-714\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-51}{-17}=3 \\x=\frac{-714}{119}=-6\end{matrix}\right.\\ \qquad V=\{(-6,3)\}\)
  7. \(\left\{\begin{matrix}-2x-4y=30\\-7x-6y=25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x-4y=30& \color{red}{7.} & \color{blue}{3.} \\-7x-6y=25& \color{red}{-2.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-14x+14x}-28y+12y=210-50} \\ \color{blue}{-6x+14x\underline{-12y+12y}=90-50} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-16y=160 \\8x=40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{160}{-16}=-10 \\x=\frac{40}{8}=5\end{matrix}\right.\\ \qquad V=\{(5,-10)\}\)
  8. \(\left\{\begin{matrix}-5x-7y=16\\-3x+4y=26\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-7y=16& \color{red}{3.} & \color{blue}{4.} \\-3x+4y=26& \color{red}{-5.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-15x+15x}-21y-20y=48-130} \\ \color{blue}{-20x-21x\underline{-28y+28y}=64+182} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-41y=-82 \\-41x=246\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-82}{-41}=2 \\x=\frac{246}{-41}=-6\end{matrix}\right.\\ \qquad V=\{(-6,2)\}\)
  9. \(\left\{\begin{matrix}-3x-7y=-13\\7x+5y=53\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x-7y=-13& \color{red}{7.} & \color{blue}{5.} \\7x+5y=53& \color{red}{3.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-21x+21x}-49y+15y=-91+159} \\ \color{blue}{-15x+49x\underline{-35y+35y}=-65+371} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-34y=68 \\34x=306\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{68}{-34}=-2 \\x=\frac{306}{34}=9\end{matrix}\right.\\ \qquad V=\{(9,-2)\}\)
  10. \(\left\{\begin{matrix}7x-5y=35\\10x=9y+37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x-5y=35\\10x-9y=37\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-5y=35& \color{red}{10.} & \color{blue}{9.} \\10x-9y=37& \color{red}{-7.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{70x-70x}-50y+63y=350-259} \\ \color{blue}{63x-50x\underline{-45y+45y}=315-185} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}13y=91 \\13x=130\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{91}{13}=7 \\x=\frac{130}{13}=10\end{matrix}\right.\\ \qquad V=\{(10,7)\}\)
  11. \(\left\{\begin{matrix}6y=-36+6x\\10x+9y=-73\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+6y=-36\\10x+9y=-73\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+6y=-36& \color{red}{5.} & \color{blue}{3.} \\10x+9y=-73& \color{red}{3.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}+30y+27y=-180-219} \\ \color{blue}{-18x-20x\underline{+18y-18y}=-108+146} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}57y=-399 \\-38x=38\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-399}{57}=-7 \\x=\frac{38}{-38}=-1\end{matrix}\right.\\ \qquad V=\{(-1,-7)\}\)
  12. \(\left\{\begin{matrix}-3y=-28-2x\\-2x-9y=-20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x-3y=-28\\-2x-9y=-20\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x-3y=-28& \color{red}{1.} & \color{blue}{3.} \\-2x-9y=-20& \color{red}{1.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{2x-2x}-3y-9y=-28-20} \\ \color{blue}{6x+2x\underline{-9y+9y}=-84+20} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-12y=-48 \\8x=-64\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-48}{-12}=4 \\x=\frac{-64}{8}=-8\end{matrix}\right.\\ \qquad V=\{(-8,4)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-12-12 02:19:45