Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}5y-8x=34\\-10x+4y=20\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}8y-7x=36\\8x+4y=64\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}9y-8x=77\\-3x-5y=-13\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-5y-8x=33\\-7x+10y=72\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-6x+4y=-44\\5y-3x=-46\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-4x-3y=-12\\7y-8x=-76\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}8x+8y=112\\-4y-4x=-56\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}10y=88-2x\\4x-6y=-58\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}8y-8x=48\\-4x-3y=-25\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-10y=-15-9x\\10x+4y=74\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}-9x-10y=-117\\-7x+7y=42\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-6x-8y=-52\\7y-10x=-107\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}5y-8x=34\\-10x+4y=20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+5y=34\\-10x+4y=20\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+5y=34& \color{red}{5.} & \color{blue}{4.} \\-10x+4y=20& \color{red}{-4.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-40x+40x}+25y-16y=170-80} \\ \color{blue}{-32x+50x\underline{+20y-20y}=136-100} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9y=90 \\18x=36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{90}{9}=10 \\x=\frac{36}{18}=2\end{matrix}\right.\\ \qquad V=\{(2,10)\}\)
  2. \(\left\{\begin{matrix}8y-7x=36\\8x+4y=64\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x+8y=36\\8x+4y=64\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x+8y=36& \color{red}{8.} & \color{blue}{1.} \\8x+4y=64& \color{red}{7.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-56x+56x}+64y+28y=288+448} \\ \color{blue}{-7x-16x\underline{+8y-8y}=36-128} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}92y=736 \\-23x=-92\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{736}{92}=8 \\x=\frac{-92}{-23}=4\end{matrix}\right.\\ \qquad V=\{(4,8)\}\)
  3. \(\left\{\begin{matrix}9y-8x=77\\-3x-5y=-13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+9y=77\\-3x-5y=-13\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+9y=77& \color{red}{3.} & \color{blue}{5.} \\-3x-5y=-13& \color{red}{-8.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}+27y+40y=231+104} \\ \color{blue}{-40x-27x\underline{+45y-45y}=385-117} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}67y=335 \\-67x=268\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{335}{67}=5 \\x=\frac{268}{-67}=-4\end{matrix}\right.\\ \qquad V=\{(-4,5)\}\)
  4. \(\left\{\begin{matrix}-5y-8x=33\\-7x+10y=72\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-5y=33\\-7x+10y=72\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-5y=33& \color{red}{7.} & \color{blue}{2.} \\-7x+10y=72& \color{red}{-8.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-56x+56x}-35y-80y=231-576} \\ \color{blue}{-16x-7x\underline{-10y+10y}=66+72} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-115y=-345 \\-23x=138\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-345}{-115}=3 \\x=\frac{138}{-23}=-6\end{matrix}\right.\\ \qquad V=\{(-6,3)\}\)
  5. \(\left\{\begin{matrix}-6x+4y=-44\\5y-3x=-46\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+4y=-44\\-3x+5y=-46\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+4y=-44& \color{red}{1.} & \color{blue}{5.} \\-3x+5y=-46& \color{red}{-2.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+4y-10y=-44+92} \\ \color{blue}{-30x+12x\underline{+20y-20y}=-220+184} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6y=48 \\-18x=-36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{48}{-6}=-8 \\x=\frac{-36}{-18}=2\end{matrix}\right.\\ \qquad V=\{(2,-8)\}\)
  6. \(\left\{\begin{matrix}-4x-3y=-12\\7y-8x=-76\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-3y=-12\\-8x+7y=-76\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x-3y=-12& \color{red}{2.} & \color{blue}{7.} \\-8x+7y=-76& \color{red}{-1.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}-6y-7y=-24+76} \\ \color{blue}{-28x-24x\underline{-21y+21y}=-84-228} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-13y=52 \\-52x=-312\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{52}{-13}=-4 \\x=\frac{-312}{-52}=6\end{matrix}\right.\\ \qquad V=\{(6,-4)\}\)
  7. \(\left\{\begin{matrix}8x+8y=112\\-4y-4x=-56\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x+8y=112\\-4x-4y=-56\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+8y=112& \color{red}{1.} & \color{blue}{1.} \\-4x-4y=-56& \color{red}{2.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}+8y-8y=112-112} \\ \color{blue}{8x-8x\underline{+8y-8y}=112-112} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}0y=0 \\0x=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{0}{0}=7 \\x=\frac{0}{0}=7\end{matrix}\right.\\ \qquad V=\{(7,7)\}\)
  8. \(\left\{\begin{matrix}10y=88-2x\\4x-6y=-58\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+10y=88\\4x-6y=-58\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+10y=88& \color{red}{2.} & \color{blue}{3.} \\4x-6y=-58& \color{red}{-1.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{4x-4x}+20y+6y=176+58} \\ \color{blue}{6x+20x\underline{+30y-30y}=264-290} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}26y=234 \\26x=-26\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{234}{26}=9 \\x=\frac{-26}{26}=-1\end{matrix}\right.\\ \qquad V=\{(-1,9)\}\)
  9. \(\left\{\begin{matrix}8y-8x=48\\-4x-3y=-25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+8y=48\\-4x-3y=-25\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+8y=48& \color{red}{1.} & \color{blue}{3.} \\-4x-3y=-25& \color{red}{-2.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}+8y+6y=48+50} \\ \color{blue}{-24x-32x\underline{+24y-24y}=144-200} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}14y=98 \\-56x=-56\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{98}{14}=7 \\x=\frac{-56}{-56}=1\end{matrix}\right.\\ \qquad V=\{(1,7)\}\)
  10. \(\left\{\begin{matrix}-10y=-15-9x\\10x+4y=74\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x-10y=-15\\10x+4y=74\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x-10y=-15& \color{red}{10.} & \color{blue}{2.} \\10x+4y=74& \color{red}{-9.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{90x-90x}-100y-36y=-150-666} \\ \color{blue}{18x+50x\underline{-20y+20y}=-30+370} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-136y=-816 \\68x=340\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-816}{-136}=6 \\x=\frac{340}{68}=5\end{matrix}\right.\\ \qquad V=\{(5,6)\}\)
  11. \(\left\{\begin{matrix}-9x-10y=-117\\-7x+7y=42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x-10y=-117& \color{red}{7.} & \color{blue}{7.} \\-7x+7y=42& \color{red}{-9.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-63x+63x}-70y-63y=-819-378} \\ \color{blue}{-63x-70x\underline{-70y+70y}=-819+420} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-133y=-1197 \\-133x=-399\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-1197}{-133}=9 \\x=\frac{-399}{-133}=3\end{matrix}\right.\\ \qquad V=\{(3,9)\}\)
  12. \(\left\{\begin{matrix}-6x-8y=-52\\7y-10x=-107\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x-8y=-52\\-10x+7y=-107\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-8y=-52& \color{red}{5.} & \color{blue}{7.} \\-10x+7y=-107& \color{red}{-3.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}-40y-21y=-260+321} \\ \color{blue}{-42x-80x\underline{-56y+56y}=-364-856} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-61y=61 \\-122x=-1220\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{61}{-61}=-1 \\x=\frac{-1220}{-122}=10\end{matrix}\right.\\ \qquad V=\{(10,-1)\}\)
Oefeningengenerator wiskundeoefeningen.be 2025-11-07 17:03:10
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