Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}-5x-10y=55\\5x=-7y-37\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}10x-7y=31\\-8y+5x=-16\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}7y+5x=64\\-4x-2y=-44\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}10y+7x=-113\\2x+9y=-63\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-6x+4y=66\\-6x=-8y+78\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-9x+3y=39\\8y-9x=74\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}9y=71+2x\\3x+3y=9\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-8x+4y=68\\-10x+6y=88\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}9x+4y=-61\\3x=5y-52\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}6x-5y=-31\\-7x=-4y+27\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}-2y+10x=104\\2x-6y=32\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-3x+2y=31\\-7y-10x=35\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}-5x-10y=55\\5x=-7y-37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-10y=55\\5x+7y=-37\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-10y=55& \color{red}{1.} & \color{blue}{7.} \\5x+7y=-37& \color{red}{1.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-5x+5x}-10y+7y=55-37} \\ \color{blue}{-35x+50x\underline{-70y+70y}=385-370} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3y=18 \\15x=15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{18}{-3}=-6 \\x=\frac{15}{15}=1\end{matrix}\right.\\ \qquad V=\{(1,-6)\}\)
  2. \(\left\{\begin{matrix}10x-7y=31\\-8y+5x=-16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x-7y=31\\5x-8y=-16\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-7y=31& \color{red}{1.} & \color{blue}{8.} \\5x-8y=-16& \color{red}{-2.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-7y+16y=31+32} \\ \color{blue}{80x-35x\underline{-56y+56y}=248+112} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9y=63 \\45x=360\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{63}{9}=7 \\x=\frac{360}{45}=8\end{matrix}\right.\\ \qquad V=\{(8,7)\}\)
  3. \(\left\{\begin{matrix}7y+5x=64\\-4x-2y=-44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x+7y=64\\-4x-2y=-44\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x+7y=64& \color{red}{4.} & \color{blue}{2.} \\-4x-2y=-44& \color{red}{5.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}+28y-10y=256-220} \\ \color{blue}{10x-28x\underline{+14y-14y}=128-308} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}18y=36 \\-18x=-180\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{36}{18}=2 \\x=\frac{-180}{-18}=10\end{matrix}\right.\\ \qquad V=\{(10,2)\}\)
  4. \(\left\{\begin{matrix}10y+7x=-113\\2x+9y=-63\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+10y=-113\\2x+9y=-63\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+10y=-113& \color{red}{2.} & \color{blue}{9.} \\2x+9y=-63& \color{red}{-7.} & \color{blue}{-10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{14x-14x}+20y-63y=-226+441} \\ \color{blue}{63x-20x\underline{+90y-90y}=-1017+630} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-43y=215 \\43x=-387\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{215}{-43}=-5 \\x=\frac{-387}{43}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-5)\}\)
  5. \(\left\{\begin{matrix}-6x+4y=66\\-6x=-8y+78\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+4y=66\\-6x+8y=78\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+4y=66& \color{red}{1.} & \color{blue}{2.} \\-6x+8y=78& \color{red}{-1.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+4y-8y=66-78} \\ \color{blue}{-12x+6x\underline{+8y-8y}=132-78} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4y=-12 \\-6x=54\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-12}{-4}=3 \\x=\frac{54}{-6}=-9\end{matrix}\right.\\ \qquad V=\{(-9,3)\}\)
  6. \(\left\{\begin{matrix}-9x+3y=39\\8y-9x=74\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x+3y=39\\-9x+8y=74\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+3y=39& \color{red}{1.} & \color{blue}{8.} \\-9x+8y=74& \color{red}{-1.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-9x+9x}+3y-8y=39-74} \\ \color{blue}{-72x+27x\underline{+24y-24y}=312-222} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5y=-35 \\-45x=90\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-35}{-5}=7 \\x=\frac{90}{-45}=-2\end{matrix}\right.\\ \qquad V=\{(-2,7)\}\)
  7. \(\left\{\begin{matrix}9y=71+2x\\3x+3y=9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+9y=71\\3x+3y=9\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+9y=71& \color{red}{3.} & \color{blue}{1.} \\3x+3y=9& \color{red}{2.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+27y+6y=213+18} \\ \color{blue}{-2x-9x\underline{+9y-9y}=71-27} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}33y=231 \\-11x=44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{231}{33}=7 \\x=\frac{44}{-11}=-4\end{matrix}\right.\\ \qquad V=\{(-4,7)\}\)
  8. \(\left\{\begin{matrix}-8x+4y=68\\-10x+6y=88\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+4y=68& \color{red}{5.} & \color{blue}{3.} \\-10x+6y=88& \color{red}{-4.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-40x+40x}+20y-24y=340-352} \\ \color{blue}{-24x+20x\underline{+12y-12y}=204-176} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4y=-12 \\-4x=28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-12}{-4}=3 \\x=\frac{28}{-4}=-7\end{matrix}\right.\\ \qquad V=\{(-7,3)\}\)
  9. \(\left\{\begin{matrix}9x+4y=-61\\3x=5y-52\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x+4y=-61\\3x-5y=-52\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+4y=-61& \color{red}{1.} & \color{blue}{5.} \\3x-5y=-52& \color{red}{-3.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{9x-9x}+4y+15y=-61+156} \\ \color{blue}{45x+12x\underline{+20y-20y}=-305-208} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}19y=95 \\57x=-513\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{95}{19}=5 \\x=\frac{-513}{57}=-9\end{matrix}\right.\\ \qquad V=\{(-9,5)\}\)
  10. \(\left\{\begin{matrix}6x-5y=-31\\-7x=-4y+27\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x-5y=-31\\-7x+4y=27\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-5y=-31& \color{red}{7.} & \color{blue}{4.} \\-7x+4y=27& \color{red}{6.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{42x-42x}-35y+24y=-217+162} \\ \color{blue}{24x-35x\underline{-20y+20y}=-124+135} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-11y=-55 \\-11x=11\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-55}{-11}=5 \\x=\frac{11}{-11}=-1\end{matrix}\right.\\ \qquad V=\{(-1,5)\}\)
  11. \(\left\{\begin{matrix}-2y+10x=104\\2x-6y=32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x-2y=104\\2x-6y=32\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-2y=104& \color{red}{1.} & \color{blue}{3.} \\2x-6y=32& \color{red}{-5.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-2y+30y=104-160} \\ \color{blue}{30x-2x\underline{-6y+6y}=312-32} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}28y=-56 \\28x=280\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-56}{28}=-2 \\x=\frac{280}{28}=10\end{matrix}\right.\\ \qquad V=\{(10,-2)\}\)
  12. \(\left\{\begin{matrix}-3x+2y=31\\-7y-10x=35\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+2y=31\\-10x-7y=35\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+2y=31& \color{red}{10.} & \color{blue}{7.} \\-10x-7y=35& \color{red}{-3.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}+20y+21y=310-105} \\ \color{blue}{-21x-20x\underline{+14y-14y}=217+70} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}41y=205 \\-41x=287\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{205}{41}=5 \\x=\frac{287}{-41}=-7\end{matrix}\right.\\ \qquad V=\{(-7,5)\}\)
Oefeningengenerator wiskundeoefeningen.be 2025-10-18 11:26:11
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