Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}2y=6+2x\\10x-4y=0\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}7x+6y=26\\-6x=-3y+51\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}4x-4y=-4\\7x+2y=56\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-2x+9y=-40\\8x+4y=0\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-6y=-10+8x\\-3x-9y=57\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}6y+2x=30\\-7x+10y=-12\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}3y-4x=21\\8x+4y=-92\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-3y=-35-8x\\-5x+5y=0\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}9y=42+4x\\-3x-8y=2\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}10y=-50+8x\\5x+7y=-88\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}5x-10y=-5\\-2y-7x=-73\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}8x-9y=5\\-8x=5y+65\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}2y=6+2x\\10x-4y=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+2y=6\\10x-4y=0\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+2y=6& \color{red}{5.} & \color{blue}{2.} \\10x-4y=0& \color{red}{1.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}+10y-4y=30+0} \\ \color{blue}{-4x+10x\underline{+4y-4y}=12+0} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6y=30 \\6x=12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{30}{6}=5 \\x=\frac{12}{6}=2\end{matrix}\right.\\ \qquad V=\{(2,5)\}\)
  2. \(\left\{\begin{matrix}7x+6y=26\\-6x=-3y+51\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+6y=26\\-6x+3y=51\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+6y=26& \color{red}{6.} & \color{blue}{1.} \\-6x+3y=51& \color{red}{7.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{42x-42x}+36y+21y=156+357} \\ \color{blue}{7x+12x\underline{+6y-6y}=26-102} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}57y=513 \\19x=-76\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{513}{57}=9 \\x=\frac{-76}{19}=-4\end{matrix}\right.\\ \qquad V=\{(-4,9)\}\)
  3. \(\left\{\begin{matrix}4x-4y=-4\\7x+2y=56\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x-4y=-4& \color{red}{7.} & \color{blue}{1.} \\7x+2y=56& \color{red}{-4.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{28x-28x}-28y-8y=-28-224} \\ \color{blue}{4x+14x\underline{-4y+4y}=-4+112} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-36y=-252 \\18x=108\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-252}{-36}=7 \\x=\frac{108}{18}=6\end{matrix}\right.\\ \qquad V=\{(6,7)\}\)
  4. \(\left\{\begin{matrix}-2x+9y=-40\\8x+4y=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+9y=-40& \color{red}{4.} & \color{blue}{4.} \\8x+4y=0& \color{red}{1.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}+36y+4y=-160+0} \\ \color{blue}{-8x-72x\underline{+36y-36y}=-160+0} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}40y=-160 \\-80x=-160\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-160}{40}=-4 \\x=\frac{-160}{-80}=2\end{matrix}\right.\\ \qquad V=\{(2,-4)\}\)
  5. \(\left\{\begin{matrix}-6y=-10+8x\\-3x-9y=57\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-6y=-10\\-3x-9y=57\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-6y=-10& \color{red}{3.} & \color{blue}{3.} \\-3x-9y=57& \color{red}{-8.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}-18y+72y=-30-456} \\ \color{blue}{-24x+6x\underline{-18y+18y}=-30-114} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}54y=-486 \\-18x=-144\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-486}{54}=-9 \\x=\frac{-144}{-18}=8\end{matrix}\right.\\ \qquad V=\{(8,-9)\}\)
  6. \(\left\{\begin{matrix}6y+2x=30\\-7x+10y=-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+6y=30\\-7x+10y=-12\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+6y=30& \color{red}{7.} & \color{blue}{5.} \\-7x+10y=-12& \color{red}{2.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{14x-14x}+42y+20y=210-24} \\ \color{blue}{10x+21x\underline{+30y-30y}=150+36} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}62y=186 \\31x=186\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{186}{62}=3 \\x=\frac{186}{31}=6\end{matrix}\right.\\ \qquad V=\{(6,3)\}\)
  7. \(\left\{\begin{matrix}3y-4x=21\\8x+4y=-92\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+3y=21\\8x+4y=-92\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x+3y=21& \color{red}{2.} & \color{blue}{4.} \\8x+4y=-92& \color{red}{1.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}+6y+4y=42-92} \\ \color{blue}{-16x-24x\underline{+12y-12y}=84+276} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10y=-50 \\-40x=360\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-50}{10}=-5 \\x=\frac{360}{-40}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-5)\}\)
  8. \(\left\{\begin{matrix}-3y=-35-8x\\-5x+5y=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x-3y=-35\\-5x+5y=0\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-3y=-35& \color{red}{5.} & \color{blue}{5.} \\-5x+5y=0& \color{red}{8.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}-15y+40y=-175+0} \\ \color{blue}{40x-15x\underline{-15y+15y}=-175+0} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}25y=-175 \\25x=-175\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-175}{25}=-7 \\x=\frac{-175}{25}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-7)\}\)
  9. \(\left\{\begin{matrix}9y=42+4x\\-3x-8y=2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+9y=42\\-3x-8y=2\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x+9y=42& \color{red}{3.} & \color{blue}{8.} \\-3x-8y=2& \color{red}{-4.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-12x+12x}+27y+32y=126-8} \\ \color{blue}{-32x-27x\underline{+72y-72y}=336+18} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}59y=118 \\-59x=354\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{118}{59}=2 \\x=\frac{354}{-59}=-6\end{matrix}\right.\\ \qquad V=\{(-6,2)\}\)
  10. \(\left\{\begin{matrix}10y=-50+8x\\5x+7y=-88\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+10y=-50\\5x+7y=-88\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+10y=-50& \color{red}{5.} & \color{blue}{7.} \\5x+7y=-88& \color{red}{8.} & \color{blue}{-10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-40x+40x}+50y+56y=-250-704} \\ \color{blue}{-56x-50x\underline{+70y-70y}=-350+880} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}106y=-954 \\-106x=530\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-954}{106}=-9 \\x=\frac{530}{-106}=-5\end{matrix}\right.\\ \qquad V=\{(-5,-9)\}\)
  11. \(\left\{\begin{matrix}5x-10y=-5\\-2y-7x=-73\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-10y=-5\\-7x-2y=-73\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-10y=-5& \color{red}{7.} & \color{blue}{1.} \\-7x-2y=-73& \color{red}{5.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{35x-35x}-70y-10y=-35-365} \\ \color{blue}{5x+35x\underline{-10y+10y}=-5+365} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-80y=-400 \\40x=360\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-400}{-80}=5 \\x=\frac{360}{40}=9\end{matrix}\right.\\ \qquad V=\{(9,5)\}\)
  12. \(\left\{\begin{matrix}8x-9y=5\\-8x=5y+65\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x-9y=5\\-8x-5y=65\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-9y=5& \color{red}{1.} & \color{blue}{5.} \\-8x-5y=65& \color{red}{1.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}-9y-5y=5+65} \\ \color{blue}{40x+72x\underline{-45y+45y}=25-585} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-14y=70 \\112x=-560\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{70}{-14}=-5 \\x=\frac{-560}{112}=-5\end{matrix}\right.\\ \qquad V=\{(-5,-5)\}\)
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