Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}8y=-48+8x\\-2x+4y=-10\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}-10x-2y=-40\\-10x=-6y-80\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}10x-10y=100\\-4y+9x=55\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}9y=72+2x\\6x+5y=-24\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}4y+4x=20\\10x+10y=50\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-3x-10y=97\\6y+6x=-54\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-7y+7x=-14\\6x+10y=-28\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}9x-2y=-30\\-5y-4x=-22\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}9x-5y=75\\-9x=4y-102\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-2x-4y=4\\3x=-2y+6\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}6x-10y=-6\\8x=8y+24\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}9x+2y=78\\9x-10y=150\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}8y=-48+8x\\-2x+4y=-10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+8y=-48\\-2x+4y=-10\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+8y=-48& \color{red}{1.} & \color{blue}{1.} \\-2x+4y=-10& \color{red}{-4.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}+8y-16y=-48+40} \\ \color{blue}{-8x+4x\underline{+8y-8y}=-48+20} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8y=-8 \\-4x=-28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-8}{-8}=1 \\x=\frac{-28}{-4}=7\end{matrix}\right.\\ \qquad V=\{(7,1)\}\)
  2. \(\left\{\begin{matrix}-10x-2y=-40\\-10x=-6y-80\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x-2y=-40\\-10x+6y=-80\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x-2y=-40& \color{red}{1.} & \color{blue}{3.} \\-10x+6y=-80& \color{red}{-1.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}-2y-6y=-40+80} \\ \color{blue}{-30x-10x\underline{-6y+6y}=-120-80} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8y=40 \\-40x=-200\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{40}{-8}=-5 \\x=\frac{-200}{-40}=5\end{matrix}\right.\\ \qquad V=\{(5,-5)\}\)
  3. \(\left\{\begin{matrix}10x-10y=100\\-4y+9x=55\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x-10y=100\\9x-4y=55\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-10y=100& \color{red}{9.} & \color{blue}{2.} \\9x-4y=55& \color{red}{-10.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{90x-90x}-90y+40y=900-550} \\ \color{blue}{20x-45x\underline{-20y+20y}=200-275} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-50y=350 \\-25x=-75\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{350}{-50}=-7 \\x=\frac{-75}{-25}=3\end{matrix}\right.\\ \qquad V=\{(3,-7)\}\)
  4. \(\left\{\begin{matrix}9y=72+2x\\6x+5y=-24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+9y=72\\6x+5y=-24\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+9y=72& \color{red}{3.} & \color{blue}{5.} \\6x+5y=-24& \color{red}{1.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+27y+5y=216-24} \\ \color{blue}{-10x-54x\underline{+45y-45y}=360+216} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}32y=192 \\-64x=576\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{192}{32}=6 \\x=\frac{576}{-64}=-9\end{matrix}\right.\\ \qquad V=\{(-9,6)\}\)
  5. \(\left\{\begin{matrix}4y+4x=20\\10x+10y=50\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+4y=20\\10x+10y=50\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+4y=20& \color{red}{5.} & \color{blue}{5.} \\10x+10y=50& \color{red}{-2.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}+20y-20y=100-100} \\ \color{blue}{20x-20x\underline{+20y-20y}=100-100} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}0y=0 \\0x=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{0}{0}=2 \\x=\frac{0}{0}=3\end{matrix}\right.\\ \qquad V=\{(3,2)\}\)
  6. \(\left\{\begin{matrix}-3x-10y=97\\6y+6x=-54\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x-10y=97\\6x+6y=-54\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x-10y=97& \color{red}{2.} & \color{blue}{3.} \\6x+6y=-54& \color{red}{1.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}-20y+6y=194-54} \\ \color{blue}{-9x+30x\underline{-30y+30y}=291-270} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-14y=140 \\21x=21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{140}{-14}=-10 \\x=\frac{21}{21}=1\end{matrix}\right.\\ \qquad V=\{(1,-10)\}\)
  7. \(\left\{\begin{matrix}-7y+7x=-14\\6x+10y=-28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x-7y=-14\\6x+10y=-28\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-7y=-14& \color{red}{6.} & \color{blue}{10.} \\6x+10y=-28& \color{red}{-7.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{42x-42x}-42y-70y=-84+196} \\ \color{blue}{70x+42x\underline{-70y+70y}=-140-196} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-112y=112 \\112x=-336\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{112}{-112}=-1 \\x=\frac{-336}{112}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-1)\}\)
  8. \(\left\{\begin{matrix}9x-2y=-30\\-5y-4x=-22\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x-2y=-30\\-4x-5y=-22\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x-2y=-30& \color{red}{4.} & \color{blue}{5.} \\-4x-5y=-22& \color{red}{9.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{36x-36x}-8y-45y=-120-198} \\ \color{blue}{45x+8x\underline{-10y+10y}=-150+44} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-53y=-318 \\53x=-106\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-318}{-53}=6 \\x=\frac{-106}{53}=-2\end{matrix}\right.\\ \qquad V=\{(-2,6)\}\)
  9. \(\left\{\begin{matrix}9x-5y=75\\-9x=4y-102\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x-5y=75\\-9x-4y=-102\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x-5y=75& \color{red}{1.} & \color{blue}{4.} \\-9x-4y=-102& \color{red}{1.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{9x-9x}-5y-4y=75-102} \\ \color{blue}{36x+45x\underline{-20y+20y}=300+510} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9y=-27 \\81x=810\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-27}{-9}=3 \\x=\frac{810}{81}=10\end{matrix}\right.\\ \qquad V=\{(10,3)\}\)
  10. \(\left\{\begin{matrix}-2x-4y=4\\3x=-2y+6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-4y=4\\3x+2y=6\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x-4y=4& \color{red}{3.} & \color{blue}{1.} \\3x+2y=6& \color{red}{2.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}-12y+4y=12+12} \\ \color{blue}{-2x+6x\underline{-4y+4y}=4+12} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8y=24 \\4x=16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{24}{-8}=-3 \\x=\frac{16}{4}=4\end{matrix}\right.\\ \qquad V=\{(4,-3)\}\)
  11. \(\left\{\begin{matrix}6x-10y=-6\\8x=8y+24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x-10y=-6\\8x-8y=24\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-10y=-6& \color{red}{4.} & \color{blue}{4.} \\8x-8y=24& \color{red}{-3.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{24x-24x}-40y+24y=-24-72} \\ \color{blue}{24x-40x\underline{-40y+40y}=-24-120} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-16y=-96 \\-16x=-144\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-96}{-16}=6 \\x=\frac{-144}{-16}=9\end{matrix}\right.\\ \qquad V=\{(9,6)\}\)
  12. \(\left\{\begin{matrix}9x+2y=78\\9x-10y=150\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+2y=78& \color{red}{1.} & \color{blue}{5.} \\9x-10y=150& \color{red}{-1.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{9x-9x}+2y+10y=78-150} \\ \color{blue}{45x+9x\underline{+10y-10y}=390+150} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}12y=-72 \\54x=540\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-72}{12}=-6 \\x=\frac{540}{54}=10\end{matrix}\right.\\ \qquad V=\{(10,-6)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2026-03-07 03:55:49