Stelsels combinatie

Hoofdmenu Eentje per keer 

Combinatie

  1. \(\left\{\begin{matrix}-4x-8y=72\\4y-10x=-60\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}3x+4y=0\\-7x-9y=2\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}-10y=-58+4x\\6x-3y=-3\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}8x-3y=27\\-7y-4x=-73\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}8y=23-7x\\-5x+7y=9\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}4x+3y=1\\10y+10x=0\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-9x-10y=-64\\-4y-6x=-16\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}7x-7y=0\\7x+6y=13\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}-2x-8y=-28\\9y+3x=30\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-2x+10y=22\\7x-8y=31\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}-5x-2y=2\\6y-9x=90\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-6y=39+3x\\8x-2y=4\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}-4x-8y=72\\4y-10x=-60\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-8y=72\\-10x+4y=-60\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x-8y=72& \color{red}{5.} & \color{blue}{1.} \\-10x+4y=-60& \color{red}{-2.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-20x+20x}-40y-8y=360+120} \\ \color{blue}{-4x-20x\underline{-8y+8y}=72-120} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-48y=480 \\-24x=-48\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{480}{-48}=-10 \\x=\frac{-48}{-24}=2\end{matrix}\right.\\ \qquad V=\{(2,-10)\}\)
  2. \(\left\{\begin{matrix}3x+4y=0\\-7x-9y=2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+4y=0& \color{red}{7.} & \color{blue}{9.} \\-7x-9y=2& \color{red}{3.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{21x-21x}+28y-27y=0+6} \\ \color{blue}{27x-28x\underline{+36y-36y}=0+8} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=6 \\-x=8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{6}{1}=6 \\x=\frac{8}{-1}=-8\end{matrix}\right.\\ \qquad V=\{(-8,6)\}\)
  3. \(\left\{\begin{matrix}-10y=-58+4x\\6x-3y=-3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-10y=-58\\6x-3y=-3\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x-10y=-58& \color{red}{3.} & \color{blue}{3.} \\6x-3y=-3& \color{red}{2.} & \color{blue}{-10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-12x+12x}-30y-6y=-174-6} \\ \color{blue}{-12x-60x\underline{-30y+30y}=-174+30} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-36y=-180 \\-72x=-144\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-180}{-36}=5 \\x=\frac{-144}{-72}=2\end{matrix}\right.\\ \qquad V=\{(2,5)\}\)
  4. \(\left\{\begin{matrix}8x-3y=27\\-7y-4x=-73\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x-3y=27\\-4x-7y=-73\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-3y=27& \color{red}{1.} & \color{blue}{7.} \\-4x-7y=-73& \color{red}{2.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}-3y-14y=27-146} \\ \color{blue}{56x+12x\underline{-21y+21y}=189+219} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-17y=-119 \\68x=408\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-119}{-17}=7 \\x=\frac{408}{68}=6\end{matrix}\right.\\ \qquad V=\{(6,7)\}\)
  5. \(\left\{\begin{matrix}8y=23-7x\\-5x+7y=9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+8y=23\\-5x+7y=9\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+8y=23& \color{red}{5.} & \color{blue}{7.} \\-5x+7y=9& \color{red}{7.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{35x-35x}+40y+49y=115+63} \\ \color{blue}{49x+40x\underline{+56y-56y}=161-72} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}89y=178 \\89x=89\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{178}{89}=2 \\x=\frac{89}{89}=1\end{matrix}\right.\\ \qquad V=\{(1,2)\}\)
  6. \(\left\{\begin{matrix}4x+3y=1\\10y+10x=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+3y=1\\10x+10y=0\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+3y=1& \color{red}{5.} & \color{blue}{10.} \\10x+10y=0& \color{red}{-2.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}+15y-20y=5+0} \\ \color{blue}{40x-30x\underline{+30y-30y}=10+0} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5y=5 \\10x=10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{5}{-5}=-1 \\x=\frac{10}{10}=1\end{matrix}\right.\\ \qquad V=\{(1,-1)\}\)
  7. \(\left\{\begin{matrix}-9x-10y=-64\\-4y-6x=-16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x-10y=-64\\-6x-4y=-16\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x-10y=-64& \color{red}{2.} & \color{blue}{2.} \\-6x-4y=-16& \color{red}{-3.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}-20y+12y=-128+48} \\ \color{blue}{-18x+30x\underline{-20y+20y}=-128+80} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8y=-80 \\12x=-48\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-80}{-8}=10 \\x=\frac{-48}{12}=-4\end{matrix}\right.\\ \qquad V=\{(-4,10)\}\)
  8. \(\left\{\begin{matrix}7x-7y=0\\7x+6y=13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-7y=0& \color{red}{1.} & \color{blue}{6.} \\7x+6y=13& \color{red}{-1.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{7x-7x}-7y-6y=0-13} \\ \color{blue}{42x+49x\underline{-42y+42y}=0+91} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-13y=-13 \\91x=91\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-13}{-13}=1 \\x=\frac{91}{91}=1\end{matrix}\right.\\ \qquad V=\{(1,1)\}\)
  9. \(\left\{\begin{matrix}-2x-8y=-28\\9y+3x=30\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-8y=-28\\3x+9y=30\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x-8y=-28& \color{red}{3.} & \color{blue}{9.} \\3x+9y=30& \color{red}{2.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}-24y+18y=-84+60} \\ \color{blue}{-18x+24x\underline{-72y+72y}=-252+240} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6y=-24 \\6x=-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-24}{-6}=4 \\x=\frac{-12}{6}=-2\end{matrix}\right.\\ \qquad V=\{(-2,4)\}\)
  10. \(\left\{\begin{matrix}-2x+10y=22\\7x-8y=31\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+10y=22& \color{red}{7.} & \color{blue}{4.} \\7x-8y=31& \color{red}{2.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-14x+14x}+70y-16y=154+62} \\ \color{blue}{-8x+35x\underline{+40y-40y}=88+155} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}54y=216 \\27x=243\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{216}{54}=4 \\x=\frac{243}{27}=9\end{matrix}\right.\\ \qquad V=\{(9,4)\}\)
  11. \(\left\{\begin{matrix}-5x-2y=2\\6y-9x=90\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-2y=2\\-9x+6y=90\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-2y=2& \color{red}{9.} & \color{blue}{3.} \\-9x+6y=90& \color{red}{-5.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-45x+45x}-18y-30y=18-450} \\ \color{blue}{-15x-9x\underline{-6y+6y}=6+90} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-48y=-432 \\-24x=96\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-432}{-48}=9 \\x=\frac{96}{-24}=-4\end{matrix}\right.\\ \qquad V=\{(-4,9)\}\)
  12. \(\left\{\begin{matrix}-6y=39+3x\\8x-2y=4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x-6y=39\\8x-2y=4\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x-6y=39& \color{red}{8.} & \color{blue}{1.} \\8x-2y=4& \color{red}{3.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}-48y-6y=312+12} \\ \color{blue}{-3x-24x\underline{-6y+6y}=39-12} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-54y=324 \\-27x=27\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{324}{-54}=-6 \\x=\frac{27}{-27}=-1\end{matrix}\right.\\ \qquad V=\{(-1,-6)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-04-26 18:21:35