Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}-3x+9y=36\\10y-4x=42\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}-6x-2y=-58\\6x+9y=93\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}10x-5y=-30\\-7x+2y=36\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-8x-6y=-132\\-3y+10x=60\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}2y=-6-4x\\-9x-5y=14\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}9y+10x=-32\\-10x-10y=30\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-8y=-15-9x\\3x-3y=-3\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-10y=53+7x\\-2x+8y=26\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}5x+2y=-39\\8x-9y=-99\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}3y=20+7x\\7x-7y=-56\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}5x+4y=61\\2y+8x=58\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}6y=46-8x\\2x+8y=18\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}-3x+9y=36\\10y-4x=42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+9y=36\\-4x+10y=42\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+9y=36& \color{red}{4.} & \color{blue}{10.} \\-4x+10y=42& \color{red}{-3.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-12x+12x}+36y-30y=144-126} \\ \color{blue}{-30x+36x\underline{+90y-90y}=360-378} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6y=18 \\6x=-18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{18}{6}=3 \\x=\frac{-18}{6}=-3\end{matrix}\right.\\ \qquad V=\{(-3,3)\}\)
  2. \(\left\{\begin{matrix}-6x-2y=-58\\6x+9y=93\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-2y=-58& \color{red}{1.} & \color{blue}{9.} \\6x+9y=93& \color{red}{1.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}-2y+9y=-58+93} \\ \color{blue}{-54x+12x\underline{-18y+18y}=-522+186} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7y=35 \\-42x=-336\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{35}{7}=5 \\x=\frac{-336}{-42}=8\end{matrix}\right.\\ \qquad V=\{(8,5)\}\)
  3. \(\left\{\begin{matrix}10x-5y=-30\\-7x+2y=36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-5y=-30& \color{red}{7.} & \color{blue}{2.} \\-7x+2y=36& \color{red}{10.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{70x-70x}-35y+20y=-210+360} \\ \color{blue}{20x-35x\underline{-10y+10y}=-60+180} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-15y=150 \\-15x=120\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{150}{-15}=-10 \\x=\frac{120}{-15}=-8\end{matrix}\right.\\ \qquad V=\{(-8,-10)\}\)
  4. \(\left\{\begin{matrix}-8x-6y=-132\\-3y+10x=60\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-6y=-132\\10x-3y=60\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-6y=-132& \color{red}{5.} & \color{blue}{1.} \\10x-3y=60& \color{red}{4.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-40x+40x}-30y-12y=-660+240} \\ \color{blue}{-8x-20x\underline{-6y+6y}=-132-120} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-42y=-420 \\-28x=-252\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-420}{-42}=10 \\x=\frac{-252}{-28}=9\end{matrix}\right.\\ \qquad V=\{(9,10)\}\)
  5. \(\left\{\begin{matrix}2y=-6-4x\\-9x-5y=14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+2y=-6\\-9x-5y=14\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+2y=-6& \color{red}{9.} & \color{blue}{5.} \\-9x-5y=14& \color{red}{4.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{36x-36x}+18y-20y=-54+56} \\ \color{blue}{20x-18x\underline{+10y-10y}=-30+28} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2y=2 \\2x=-2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{2}{-2}=-1 \\x=\frac{-2}{2}=-1\end{matrix}\right.\\ \qquad V=\{(-1,-1)\}\)
  6. \(\left\{\begin{matrix}9y+10x=-32\\-10x-10y=30\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x+9y=-32\\-10x-10y=30\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x+9y=-32& \color{red}{1.} & \color{blue}{10.} \\-10x-10y=30& \color{red}{1.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}+9y-10y=-32+30} \\ \color{blue}{100x-90x\underline{+90y-90y}=-320+270} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-y=-2 \\10x=-50\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-2}{-1}=2 \\x=\frac{-50}{10}=-5\end{matrix}\right.\\ \qquad V=\{(-5,2)\}\)
  7. \(\left\{\begin{matrix}-8y=-15-9x\\3x-3y=-3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x-8y=-15\\3x-3y=-3\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x-8y=-15& \color{red}{1.} & \color{blue}{3.} \\3x-3y=-3& \color{red}{-3.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{9x-9x}-8y+9y=-15+9} \\ \color{blue}{27x-24x\underline{-24y+24y}=-45+24} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-6 \\3x=-21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-6}{1}=-6 \\x=\frac{-21}{3}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-6)\}\)
  8. \(\left\{\begin{matrix}-10y=53+7x\\-2x+8y=26\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-10y=53\\-2x+8y=26\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-10y=53& \color{red}{2.} & \color{blue}{4.} \\-2x+8y=26& \color{red}{-7.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-14x+14x}-20y-56y=106-182} \\ \color{blue}{-28x-10x\underline{-40y+40y}=212+130} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-76y=-76 \\-38x=342\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-76}{-76}=1 \\x=\frac{342}{-38}=-9\end{matrix}\right.\\ \qquad V=\{(-9,1)\}\)
  9. \(\left\{\begin{matrix}5x+2y=-39\\8x-9y=-99\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x+2y=-39& \color{red}{8.} & \color{blue}{9.} \\8x-9y=-99& \color{red}{-5.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}+16y+45y=-312+495} \\ \color{blue}{45x+16x\underline{+18y-18y}=-351-198} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}61y=183 \\61x=-549\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{183}{61}=3 \\x=\frac{-549}{61}=-9\end{matrix}\right.\\ \qquad V=\{(-9,3)\}\)
  10. \(\left\{\begin{matrix}3y=20+7x\\7x-7y=-56\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x+3y=20\\7x-7y=-56\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x+3y=20& \color{red}{1.} & \color{blue}{7.} \\7x-7y=-56& \color{red}{1.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-7x+7x}+3y-7y=20-56} \\ \color{blue}{-49x+21x\underline{+21y-21y}=140-168} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4y=-36 \\-28x=-28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-36}{-4}=9 \\x=\frac{-28}{-28}=1\end{matrix}\right.\\ \qquad V=\{(1,9)\}\)
  11. \(\left\{\begin{matrix}5x+4y=61\\2y+8x=58\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x+4y=61\\8x+2y=58\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x+4y=61& \color{red}{8.} & \color{blue}{1.} \\8x+2y=58& \color{red}{-5.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}+32y-10y=488-290} \\ \color{blue}{5x-16x\underline{+4y-4y}=61-116} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}22y=198 \\-11x=-55\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{198}{22}=9 \\x=\frac{-55}{-11}=5\end{matrix}\right.\\ \qquad V=\{(5,9)\}\)
  12. \(\left\{\begin{matrix}6y=46-8x\\2x+8y=18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x+6y=46\\2x+8y=18\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+6y=46& \color{red}{1.} & \color{blue}{4.} \\2x+8y=18& \color{red}{-4.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}+6y-32y=46-72} \\ \color{blue}{32x-6x\underline{+24y-24y}=184-54} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-26y=-26 \\26x=130\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-26}{-26}=1 \\x=\frac{130}{26}=5\end{matrix}\right.\\ \qquad V=\{(5,1)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2026-09-13 19:33:34