Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}-3x+3y=3\\-7x+7y=7\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}-5x-2y=42\\8x=5y-100\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}7x+2y=-62\\-3y+3x=-15\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}9x+5y=-26\\10x+3y=-34\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}8y+5x=59\\9x+2y=69\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-10x+7y=103\\-3x-3y=-15\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}9x-6y=-75\\5x-4y=-43\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-4x+6y=28\\5x-4y=-21\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}7y=-95+5x\\6x-6y=90\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-10y=-140-5x\\3x+7y=46\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}8x-2y=-66\\-8x=5y+59\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-5y=15+7x\\8x+3y=-28\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}-3x+3y=3\\-7x+7y=7\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+3y=3& \color{red}{7.} & \color{blue}{7.} \\-7x+7y=7& \color{red}{-3.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-21x+21x}+21y-21y=21-21} \\ \color{blue}{-21x+21x\underline{+21y-21y}=21-21} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}0y=0 \\0x=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{0}{0}=5 \\x=\frac{0}{0}=4\end{matrix}\right.\\ \qquad V=\{(4,5)\}\)
  2. \(\left\{\begin{matrix}-5x-2y=42\\8x=5y-100\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-2y=42\\8x-5y=-100\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-2y=42& \color{red}{8.} & \color{blue}{5.} \\8x-5y=-100& \color{red}{5.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-40x+40x}-16y-25y=336-500} \\ \color{blue}{-25x-16x\underline{-10y+10y}=210+200} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-41y=-164 \\-41x=410\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-164}{-41}=4 \\x=\frac{410}{-41}=-10\end{matrix}\right.\\ \qquad V=\{(-10,4)\}\)
  3. \(\left\{\begin{matrix}7x+2y=-62\\-3y+3x=-15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+2y=-62\\3x-3y=-15\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+2y=-62& \color{red}{3.} & \color{blue}{3.} \\3x-3y=-15& \color{red}{-7.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{21x-21x}+6y+21y=-186+105} \\ \color{blue}{21x+6x\underline{+6y-6y}=-186-30} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}27y=-81 \\27x=-216\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-81}{27}=-3 \\x=\frac{-216}{27}=-8\end{matrix}\right.\\ \qquad V=\{(-8,-3)\}\)
  4. \(\left\{\begin{matrix}9x+5y=-26\\10x+3y=-34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+5y=-26& \color{red}{10.} & \color{blue}{3.} \\10x+3y=-34& \color{red}{-9.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{90x-90x}+50y-27y=-260+306} \\ \color{blue}{27x-50x\underline{+15y-15y}=-78+170} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}23y=46 \\-23x=92\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{46}{23}=2 \\x=\frac{92}{-23}=-4\end{matrix}\right.\\ \qquad V=\{(-4,2)\}\)
  5. \(\left\{\begin{matrix}8y+5x=59\\9x+2y=69\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x+8y=59\\9x+2y=69\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x+8y=59& \color{red}{9.} & \color{blue}{1.} \\9x+2y=69& \color{red}{-5.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{45x-45x}+72y-10y=531-345} \\ \color{blue}{5x-36x\underline{+8y-8y}=59-276} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}62y=186 \\-31x=-217\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{186}{62}=3 \\x=\frac{-217}{-31}=7\end{matrix}\right.\\ \qquad V=\{(7,3)\}\)
  6. \(\left\{\begin{matrix}-10x+7y=103\\-3x-3y=-15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x+7y=103& \color{red}{3.} & \color{blue}{3.} \\-3x-3y=-15& \color{red}{-10.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}+21y+30y=309+150} \\ \color{blue}{-30x-21x\underline{+21y-21y}=309-105} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}51y=459 \\-51x=204\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{459}{51}=9 \\x=\frac{204}{-51}=-4\end{matrix}\right.\\ \qquad V=\{(-4,9)\}\)
  7. \(\left\{\begin{matrix}9x-6y=-75\\5x-4y=-43\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x-6y=-75& \color{red}{5.} & \color{blue}{2.} \\5x-4y=-43& \color{red}{-9.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{45x-45x}-30y+36y=-375+387} \\ \color{blue}{18x-15x\underline{-12y+12y}=-150+129} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6y=12 \\3x=-21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{12}{6}=2 \\x=\frac{-21}{3}=-7\end{matrix}\right.\\ \qquad V=\{(-7,2)\}\)
  8. \(\left\{\begin{matrix}-4x+6y=28\\5x-4y=-21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x+6y=28& \color{red}{5.} & \color{blue}{2.} \\5x-4y=-21& \color{red}{4.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-20x+20x}+30y-16y=140-84} \\ \color{blue}{-8x+15x\underline{+12y-12y}=56-63} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}14y=56 \\7x=-7\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{56}{14}=4 \\x=\frac{-7}{7}=-1\end{matrix}\right.\\ \qquad V=\{(-1,4)\}\)
  9. \(\left\{\begin{matrix}7y=-95+5x\\6x-6y=90\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+7y=-95\\6x-6y=90\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x+7y=-95& \color{red}{6.} & \color{blue}{6.} \\6x-6y=90& \color{red}{5.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}+42y-30y=-570+450} \\ \color{blue}{-30x+42x\underline{+42y-42y}=-570+630} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}12y=-120 \\12x=60\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-120}{12}=-10 \\x=\frac{60}{12}=5\end{matrix}\right.\\ \qquad V=\{(5,-10)\}\)
  10. \(\left\{\begin{matrix}-10y=-140-5x\\3x+7y=46\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-10y=-140\\3x+7y=46\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-10y=-140& \color{red}{3.} & \color{blue}{7.} \\3x+7y=46& \color{red}{-5.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{15x-15x}-30y-35y=-420-230} \\ \color{blue}{35x+30x\underline{-70y+70y}=-980+460} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-65y=-650 \\65x=-520\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-650}{-65}=10 \\x=\frac{-520}{65}=-8\end{matrix}\right.\\ \qquad V=\{(-8,10)\}\)
  11. \(\left\{\begin{matrix}8x-2y=-66\\-8x=5y+59\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x-2y=-66\\-8x-5y=59\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-2y=-66& \color{red}{1.} & \color{blue}{5.} \\-8x-5y=59& \color{red}{1.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}-2y-5y=-66+59} \\ \color{blue}{40x+16x\underline{-10y+10y}=-330-118} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7y=-7 \\56x=-448\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-7}{-7}=1 \\x=\frac{-448}{56}=-8\end{matrix}\right.\\ \qquad V=\{(-8,1)\}\)
  12. \(\left\{\begin{matrix}-5y=15+7x\\8x+3y=-28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-5y=15\\8x+3y=-28\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-5y=15& \color{red}{8.} & \color{blue}{3.} \\8x+3y=-28& \color{red}{7.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-56x+56x}-40y+21y=120-196} \\ \color{blue}{-21x+40x\underline{-15y+15y}=45-140} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-19y=-76 \\19x=-95\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-76}{-19}=4 \\x=\frac{-95}{19}=-5\end{matrix}\right.\\ \qquad V=\{(-5,4)\}\)
Oefeningengenerator wiskundeoefeningen.be 2024-11-23 10:31:01
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