Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}10y-7x=-3\\9x-5y=-4\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}-5x+3y=32\\-5y-4x=33\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}8y=48-4x\\2x-9y=11\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-10y-3x=-26\\-8x-6y=34\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-4x+9y=80\\-3y+3x=-30\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-5x-6y=-22\\5y-10x=-95\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-9y-7x=-1\\4x+7y=8\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}9x+2y=-83\\-6y-5x=95\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}-3x+3y=-21\\-10x=7y+100\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-3x+7y=44\\8y-3x=52\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}7x-7y=42\\3x+5y=-22\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}3x+9y=66\\-7x+2y=76\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}10y-7x=-3\\9x-5y=-4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x+10y=-3\\9x-5y=-4\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x+10y=-3& \color{red}{9.} & \color{blue}{1.} \\9x-5y=-4& \color{red}{7.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-63x+63x}+90y-35y=-27-28} \\ \color{blue}{-7x+18x\underline{+10y-10y}=-3-8} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}55y=-55 \\11x=-11\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-55}{55}=-1 \\x=\frac{-11}{11}=-1\end{matrix}\right.\\ \qquad V=\{(-1,-1)\}\)
  2. \(\left\{\begin{matrix}-5x+3y=32\\-5y-4x=33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+3y=32\\-4x-5y=33\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x+3y=32& \color{red}{4.} & \color{blue}{5.} \\-4x-5y=33& \color{red}{-5.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-20x+20x}+12y+25y=128-165} \\ \color{blue}{-25x-12x\underline{+15y-15y}=160+99} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}37y=-37 \\-37x=259\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-37}{37}=-1 \\x=\frac{259}{-37}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-1)\}\)
  3. \(\left\{\begin{matrix}8y=48-4x\\2x-9y=11\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+8y=48\\2x-9y=11\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+8y=48& \color{red}{1.} & \color{blue}{9.} \\2x-9y=11& \color{red}{-2.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{4x-4x}+8y+18y=48-22} \\ \color{blue}{36x+16x\underline{+72y-72y}=432+88} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}26y=26 \\52x=520\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{26}{26}=1 \\x=\frac{520}{52}=10\end{matrix}\right.\\ \qquad V=\{(10,1)\}\)
  4. \(\left\{\begin{matrix}-10y-3x=-26\\-8x-6y=34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x-10y=-26\\-8x-6y=34\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x-10y=-26& \color{red}{8.} & \color{blue}{3.} \\-8x-6y=34& \color{red}{-3.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}-80y+18y=-208-102} \\ \color{blue}{-9x+40x\underline{-30y+30y}=-78-170} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-62y=-310 \\31x=-248\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-310}{-62}=5 \\x=\frac{-248}{31}=-8\end{matrix}\right.\\ \qquad V=\{(-8,5)\}\)
  5. \(\left\{\begin{matrix}-4x+9y=80\\-3y+3x=-30\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+9y=80\\3x-3y=-30\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x+9y=80& \color{red}{3.} & \color{blue}{1.} \\3x-3y=-30& \color{red}{4.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-12x+12x}+27y-12y=240-120} \\ \color{blue}{-4x+9x\underline{+9y-9y}=80-90} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}15y=120 \\5x=-10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{120}{15}=8 \\x=\frac{-10}{5}=-2\end{matrix}\right.\\ \qquad V=\{(-2,8)\}\)
  6. \(\left\{\begin{matrix}-5x-6y=-22\\5y-10x=-95\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-6y=-22\\-10x+5y=-95\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-6y=-22& \color{red}{2.} & \color{blue}{5.} \\-10x+5y=-95& \color{red}{-1.} & \color{blue}{6.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}-12y-5y=-44+95} \\ \color{blue}{-25x-60x\underline{-30y+30y}=-110-570} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-17y=51 \\-85x=-680\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{51}{-17}=-3 \\x=\frac{-680}{-85}=8\end{matrix}\right.\\ \qquad V=\{(8,-3)\}\)
  7. \(\left\{\begin{matrix}-9y-7x=-1\\4x+7y=8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-9y=-1\\4x+7y=8\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-9y=-1& \color{red}{4.} & \color{blue}{7.} \\4x+7y=8& \color{red}{7.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-28x+28x}-36y+49y=-4+56} \\ \color{blue}{-49x+36x\underline{-63y+63y}=-7+72} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}13y=52 \\-13x=65\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{52}{13}=4 \\x=\frac{65}{-13}=-5\end{matrix}\right.\\ \qquad V=\{(-5,4)\}\)
  8. \(\left\{\begin{matrix}9x+2y=-83\\-6y-5x=95\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x+2y=-83\\-5x-6y=95\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+2y=-83& \color{red}{5.} & \color{blue}{3.} \\-5x-6y=95& \color{red}{9.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{45x-45x}+10y-54y=-415+855} \\ \color{blue}{27x-5x\underline{+6y-6y}=-249+95} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-44y=440 \\22x=-154\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{440}{-44}=-10 \\x=\frac{-154}{22}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-10)\}\)
  9. \(\left\{\begin{matrix}-3x+3y=-21\\-10x=7y+100\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+3y=-21\\-10x-7y=100\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+3y=-21& \color{red}{10.} & \color{blue}{7.} \\-10x-7y=100& \color{red}{-3.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}+30y+21y=-210-300} \\ \color{blue}{-21x-30x\underline{+21y-21y}=-147+300} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}51y=-510 \\-51x=153\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-510}{51}=-10 \\x=\frac{153}{-51}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-10)\}\)
  10. \(\left\{\begin{matrix}-3x+7y=44\\8y-3x=52\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+7y=44\\-3x+8y=52\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+7y=44& \color{red}{1.} & \color{blue}{8.} \\-3x+8y=52& \color{red}{-1.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-3x+3x}+7y-8y=44-52} \\ \color{blue}{-24x+21x\underline{+56y-56y}=352-364} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-y=-8 \\-3x=-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-8}{-1}=8 \\x=\frac{-12}{-3}=4\end{matrix}\right.\\ \qquad V=\{(4,8)\}\)
  11. \(\left\{\begin{matrix}7x-7y=42\\3x+5y=-22\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-7y=42& \color{red}{3.} & \color{blue}{5.} \\3x+5y=-22& \color{red}{-7.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{21x-21x}-21y-35y=126+154} \\ \color{blue}{35x+21x\underline{-35y+35y}=210-154} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-56y=280 \\56x=56\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{280}{-56}=-5 \\x=\frac{56}{56}=1\end{matrix}\right.\\ \qquad V=\{(1,-5)\}\)
  12. \(\left\{\begin{matrix}3x+9y=66\\-7x+2y=76\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+9y=66& \color{red}{7.} & \color{blue}{2.} \\-7x+2y=76& \color{red}{3.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{21x-21x}+63y+6y=462+228} \\ \color{blue}{6x+63x\underline{+18y-18y}=132-684} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}69y=690 \\69x=-552\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{690}{69}=10 \\x=\frac{-552}{69}=-8\end{matrix}\right.\\ \qquad V=\{(-8,10)\}\)
Oefeningengenerator wiskundeoefeningen.be 2025-04-04 07:24:42
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