Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}-2y=-36+10x\\-10x+9y=-58\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}6x-9y=-69\\-7x-8y=-49\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}10x+6y=130\\4x=2y+30\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-2x+9y=26\\8x+6y=64\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-9x+3y=30\\-2x+5y=37\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-10y-5x=-50\\-3x+5y=14\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-3y-6x=9\\-10x+8y=-102\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-4x-6y=-32\\2x=9y-32\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}-9y=-45-9x\\10x-7y=-62\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}5y=3-7x\\-3x+8y=19\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}2y=58+6x\\8x-7y=-73\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-8x-4y=-20\\-9y+5x=116\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}-2y=-36+10x\\-10x+9y=-58\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x-2y=-36\\-10x+9y=-58\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x-2y=-36& \color{red}{1.} & \color{blue}{9.} \\-10x+9y=-58& \color{red}{-1.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}-2y-9y=-36+58} \\ \color{blue}{-90x-20x\underline{-18y+18y}=-324-116} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-11y=22 \\-110x=-440\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{22}{-11}=-2 \\x=\frac{-440}{-110}=4\end{matrix}\right.\\ \qquad V=\{(4,-2)\}\)
  2. \(\left\{\begin{matrix}6x-9y=-69\\-7x-8y=-49\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-9y=-69& \color{red}{7.} & \color{blue}{8.} \\-7x-8y=-49& \color{red}{6.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{42x-42x}-63y-48y=-483-294} \\ \color{blue}{48x+63x\underline{-72y+72y}=-552+441} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-111y=-777 \\111x=-111\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-777}{-111}=7 \\x=\frac{-111}{111}=-1\end{matrix}\right.\\ \qquad V=\{(-1,7)\}\)
  3. \(\left\{\begin{matrix}10x+6y=130\\4x=2y+30\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x+6y=130\\4x-2y=30\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x+6y=130& \color{red}{2.} & \color{blue}{1.} \\4x-2y=30& \color{red}{-5.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}+12y+10y=260-150} \\ \color{blue}{10x+12x\underline{+6y-6y}=130+90} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}22y=110 \\22x=220\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{110}{22}=5 \\x=\frac{220}{22}=10\end{matrix}\right.\\ \qquad V=\{(10,5)\}\)
  4. \(\left\{\begin{matrix}-2x+9y=26\\8x+6y=64\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+9y=26& \color{red}{4.} & \color{blue}{2.} \\8x+6y=64& \color{red}{1.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}+36y+6y=104+64} \\ \color{blue}{-4x-24x\underline{+18y-18y}=52-192} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}42y=168 \\-28x=-140\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{168}{42}=4 \\x=\frac{-140}{-28}=5\end{matrix}\right.\\ \qquad V=\{(5,4)\}\)
  5. \(\left\{\begin{matrix}-9x+3y=30\\-2x+5y=37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+3y=30& \color{red}{2.} & \color{blue}{5.} \\-2x+5y=37& \color{red}{-9.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}+6y-45y=60-333} \\ \color{blue}{-45x+6x\underline{+15y-15y}=150-111} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-39y=-273 \\-39x=39\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-273}{-39}=7 \\x=\frac{39}{-39}=-1\end{matrix}\right.\\ \qquad V=\{(-1,7)\}\)
  6. \(\left\{\begin{matrix}-10y-5x=-50\\-3x+5y=14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-10y=-50\\-3x+5y=14\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-10y=-50& \color{red}{3.} & \color{blue}{1.} \\-3x+5y=14& \color{red}{-5.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-15x+15x}-30y-25y=-150-70} \\ \color{blue}{-5x-6x\underline{-10y+10y}=-50+28} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-55y=-220 \\-11x=-22\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-220}{-55}=4 \\x=\frac{-22}{-11}=2\end{matrix}\right.\\ \qquad V=\{(2,4)\}\)
  7. \(\left\{\begin{matrix}-3y-6x=9\\-10x+8y=-102\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x-3y=9\\-10x+8y=-102\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-3y=9& \color{red}{5.} & \color{blue}{8.} \\-10x+8y=-102& \color{red}{-3.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}-15y-24y=45+306} \\ \color{blue}{-48x-30x\underline{-24y+24y}=72-306} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-39y=351 \\-78x=-234\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{351}{-39}=-9 \\x=\frac{-234}{-78}=3\end{matrix}\right.\\ \qquad V=\{(3,-9)\}\)
  8. \(\left\{\begin{matrix}-4x-6y=-32\\2x=9y-32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-6y=-32\\2x-9y=-32\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x-6y=-32& \color{red}{1.} & \color{blue}{3.} \\2x-9y=-32& \color{red}{2.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-4x+4x}-6y-18y=-32-64} \\ \color{blue}{-12x-4x\underline{-18y+18y}=-96+64} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-24y=-96 \\-16x=-32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-96}{-24}=4 \\x=\frac{-32}{-16}=2\end{matrix}\right.\\ \qquad V=\{(2,4)\}\)
  9. \(\left\{\begin{matrix}-9y=-45-9x\\10x-7y=-62\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x-9y=-45\\10x-7y=-62\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x-9y=-45& \color{red}{10.} & \color{blue}{7.} \\10x-7y=-62& \color{red}{-9.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{90x-90x}-90y+63y=-450+558} \\ \color{blue}{63x-90x\underline{-63y+63y}=-315+558} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-27y=108 \\-27x=243\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{108}{-27}=-4 \\x=\frac{243}{-27}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-4)\}\)
  10. \(\left\{\begin{matrix}5y=3-7x\\-3x+8y=19\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+5y=3\\-3x+8y=19\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+5y=3& \color{red}{3.} & \color{blue}{8.} \\-3x+8y=19& \color{red}{7.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{21x-21x}+15y+56y=9+133} \\ \color{blue}{56x+15x\underline{+40y-40y}=24-95} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}71y=142 \\71x=-71\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{142}{71}=2 \\x=\frac{-71}{71}=-1\end{matrix}\right.\\ \qquad V=\{(-1,2)\}\)
  11. \(\left\{\begin{matrix}2y=58+6x\\8x-7y=-73\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+2y=58\\8x-7y=-73\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+2y=58& \color{red}{4.} & \color{blue}{7.} \\8x-7y=-73& \color{red}{3.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}+8y-21y=232-219} \\ \color{blue}{-42x+16x\underline{+14y-14y}=406-146} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-13y=13 \\-26x=260\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{13}{-13}=-1 \\x=\frac{260}{-26}=-10\end{matrix}\right.\\ \qquad V=\{(-10,-1)\}\)
  12. \(\left\{\begin{matrix}-8x-4y=-20\\-9y+5x=116\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-4y=-20\\5x-9y=116\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-4y=-20& \color{red}{5.} & \color{blue}{9.} \\5x-9y=116& \color{red}{8.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-40x+40x}-20y-72y=-100+928} \\ \color{blue}{-72x-20x\underline{-36y+36y}=-180-464} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-92y=828 \\-92x=-644\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{828}{-92}=-9 \\x=\frac{-644}{-92}=7\end{matrix}\right.\\ \qquad V=\{(7,-9)\}\)
Oefeningengenerator wiskundeoefeningen.be 2025-09-16 16:17:40
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