Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}-8y=-51-7x\\-8x+5y=21\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}-3y-7x=44\\-5x-7y=46\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}8x-5y=-50\\-8x+6y=44\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-5x+6y=7\\3y-2x=7\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}5x+10y=140\\-7x=9y-146\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-7x-5y=82\\-6x=-3y+12\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-7x+5y=-24\\5x+10y=85\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-9y-5x=-28\\10x+7y=34\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}5x-6y=22\\4y-7x=-22\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}10x-3y=-24\\-4y-2x=14\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}-2y=4-4x\\4x-3y=2\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}7y+9x=12\\2x-6y=-20\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}-8y=-51-7x\\-8x+5y=21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x-8y=-51\\-8x+5y=21\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-8y=-51& \color{red}{8.} & \color{blue}{5.} \\-8x+5y=21& \color{red}{7.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{56x-56x}-64y+35y=-408+147} \\ \color{blue}{35x-64x\underline{-40y+40y}=-255+168} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-29y=-261 \\-29x=-87\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-261}{-29}=9 \\x=\frac{-87}{-29}=3\end{matrix}\right.\\ \qquad V=\{(3,9)\}\)
  2. \(\left\{\begin{matrix}-3y-7x=44\\-5x-7y=46\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-3y=44\\-5x-7y=46\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-3y=44& \color{red}{5.} & \color{blue}{7.} \\-5x-7y=46& \color{red}{-7.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-35x+35x}-15y+49y=220-322} \\ \color{blue}{-49x+15x\underline{-21y+21y}=308-138} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}34y=-102 \\-34x=170\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-102}{34}=-3 \\x=\frac{170}{-34}=-5\end{matrix}\right.\\ \qquad V=\{(-5,-3)\}\)
  3. \(\left\{\begin{matrix}8x-5y=-50\\-8x+6y=44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-5y=-50& \color{red}{1.} & \color{blue}{6.} \\-8x+6y=44& \color{red}{1.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}-5y+6y=-50+44} \\ \color{blue}{48x-40x\underline{-30y+30y}=-300+220} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-6 \\8x=-80\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-6}{1}=-6 \\x=\frac{-80}{8}=-10\end{matrix}\right.\\ \qquad V=\{(-10,-6)\}\)
  4. \(\left\{\begin{matrix}-5x+6y=7\\3y-2x=7\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+6y=7\\-2x+3y=7\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x+6y=7& \color{red}{2.} & \color{blue}{1.} \\-2x+3y=7& \color{red}{-5.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}+12y-15y=14-35} \\ \color{blue}{-5x+4x\underline{+6y-6y}=7-14} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3y=-21 \\-x=-7\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-21}{-3}=7 \\x=\frac{-7}{-1}=7\end{matrix}\right.\\ \qquad V=\{(7,7)\}\)
  5. \(\left\{\begin{matrix}5x+10y=140\\-7x=9y-146\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x+10y=140\\-7x-9y=-146\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x+10y=140& \color{red}{7.} & \color{blue}{9.} \\-7x-9y=-146& \color{red}{5.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{35x-35x}+70y-45y=980-730} \\ \color{blue}{45x-70x\underline{+90y-90y}=1260-1460} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}25y=250 \\-25x=-200\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{250}{25}=10 \\x=\frac{-200}{-25}=8\end{matrix}\right.\\ \qquad V=\{(8,10)\}\)
  6. \(\left\{\begin{matrix}-7x-5y=82\\-6x=-3y+12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-5y=82\\-6x+3y=12\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-5y=82& \color{red}{6.} & \color{blue}{3.} \\-6x+3y=12& \color{red}{-7.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-42x+42x}-30y-21y=492-84} \\ \color{blue}{-21x-30x\underline{-15y+15y}=246+60} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-51y=408 \\-51x=306\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{408}{-51}=-8 \\x=\frac{306}{-51}=-6\end{matrix}\right.\\ \qquad V=\{(-6,-8)\}\)
  7. \(\left\{\begin{matrix}-7x+5y=-24\\5x+10y=85\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x+5y=-24& \color{red}{5.} & \color{blue}{2.} \\5x+10y=85& \color{red}{7.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-35x+35x}+25y+70y=-120+595} \\ \color{blue}{-14x-5x\underline{+10y-10y}=-48-85} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}95y=475 \\-19x=-133\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{475}{95}=5 \\x=\frac{-133}{-19}=7\end{matrix}\right.\\ \qquad V=\{(7,5)\}\)
  8. \(\left\{\begin{matrix}-9y-5x=-28\\10x+7y=34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-9y=-28\\10x+7y=34\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-9y=-28& \color{red}{2.} & \color{blue}{7.} \\10x+7y=34& \color{red}{1.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}-18y+7y=-56+34} \\ \color{blue}{-35x+90x\underline{-63y+63y}=-196+306} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-11y=-22 \\55x=110\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-22}{-11}=2 \\x=\frac{110}{55}=2\end{matrix}\right.\\ \qquad V=\{(2,2)\}\)
  9. \(\left\{\begin{matrix}5x-6y=22\\4y-7x=-22\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-6y=22\\-7x+4y=-22\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-6y=22& \color{red}{7.} & \color{blue}{2.} \\-7x+4y=-22& \color{red}{5.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{35x-35x}-42y+20y=154-110} \\ \color{blue}{10x-21x\underline{-12y+12y}=44-66} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-22y=44 \\-11x=-22\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{44}{-22}=-2 \\x=\frac{-22}{-11}=2\end{matrix}\right.\\ \qquad V=\{(2,-2)\}\)
  10. \(\left\{\begin{matrix}10x-3y=-24\\-4y-2x=14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x-3y=-24\\-2x-4y=14\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-3y=-24& \color{red}{1.} & \color{blue}{4.} \\-2x-4y=14& \color{red}{5.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-3y-20y=-24+70} \\ \color{blue}{40x+6x\underline{-12y+12y}=-96-42} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-23y=46 \\46x=-138\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{46}{-23}=-2 \\x=\frac{-138}{46}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-2)\}\)
  11. \(\left\{\begin{matrix}-2y=4-4x\\4x-3y=2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-2y=4\\4x-3y=2\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x-2y=4& \color{red}{1.} & \color{blue}{3.} \\4x-3y=2& \color{red}{-1.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{4x-4x}-2y+3y=4-2} \\ \color{blue}{12x-8x\underline{-6y+6y}=12-4} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=2 \\4x=8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{2}{1}=2 \\x=\frac{8}{4}=2\end{matrix}\right.\\ \qquad V=\{(2,2)\}\)
  12. \(\left\{\begin{matrix}7y+9x=12\\2x-6y=-20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x+7y=12\\2x-6y=-20\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+7y=12& \color{red}{2.} & \color{blue}{6.} \\2x-6y=-20& \color{red}{-9.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{18x-18x}+14y+54y=24+180} \\ \color{blue}{54x+14x\underline{+42y-42y}=72-140} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}68y=204 \\68x=-68\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{204}{68}=3 \\x=\frac{-68}{68}=-1\end{matrix}\right.\\ \qquad V=\{(-1,3)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-05-19 04:06:52