Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}3x+4y=21\\5x+3y=24\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}10x+5y=-60\\2y+7x=-39\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}-9x-10y=103\\-6y+3x=3\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-9x+7y=10\\6x-10y=20\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-8x-7y=107\\-4y-8x=92\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}8x-8y=-40\\4y+7x=-57\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}4x-6y=66\\10x=-3y+75\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-10y=59-7x\\-5x+7y=-42\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}8y=-80-3x\\-10x+3y=59\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-10x+6y=76\\-3y-9x=60\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}9x+9y=-54\\8x-3y=-26\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-9x+6y=18\\-6x+8y=-12\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}3x+4y=21\\5x+3y=24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+4y=21& \color{red}{5.} & \color{blue}{3.} \\5x+3y=24& \color{red}{-3.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{15x-15x}+20y-9y=105-72} \\ \color{blue}{9x-20x\underline{+12y-12y}=63-96} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}11y=33 \\-11x=-33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{33}{11}=3 \\x=\frac{-33}{-11}=3\end{matrix}\right.\\ \qquad V=\{(3,3)\}\)
  2. \(\left\{\begin{matrix}10x+5y=-60\\2y+7x=-39\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x+5y=-60\\7x+2y=-39\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x+5y=-60& \color{red}{7.} & \color{blue}{2.} \\7x+2y=-39& \color{red}{-10.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{70x-70x}+35y-20y=-420+390} \\ \color{blue}{20x-35x\underline{+10y-10y}=-120+195} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}15y=-30 \\-15x=75\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-30}{15}=-2 \\x=\frac{75}{-15}=-5\end{matrix}\right.\\ \qquad V=\{(-5,-2)\}\)
  3. \(\left\{\begin{matrix}-9x-10y=103\\-6y+3x=3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x-10y=103\\3x-6y=3\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x-10y=103& \color{red}{1.} & \color{blue}{3.} \\3x-6y=3& \color{red}{3.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-9x+9x}-10y-18y=103+9} \\ \color{blue}{-27x-15x\underline{-30y+30y}=309-15} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-28y=112 \\-42x=294\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{112}{-28}=-4 \\x=\frac{294}{-42}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-4)\}\)
  4. \(\left\{\begin{matrix}-9x+7y=10\\6x-10y=20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+7y=10& \color{red}{2.} & \color{blue}{10.} \\6x-10y=20& \color{red}{3.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}+14y-30y=20+60} \\ \color{blue}{-90x+42x\underline{+70y-70y}=100+140} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-16y=80 \\-48x=240\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{80}{-16}=-5 \\x=\frac{240}{-48}=-5\end{matrix}\right.\\ \qquad V=\{(-5,-5)\}\)
  5. \(\left\{\begin{matrix}-8x-7y=107\\-4y-8x=92\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-7y=107\\-8x-4y=92\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-7y=107& \color{red}{1.} & \color{blue}{4.} \\-8x-4y=92& \color{red}{-1.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}-7y+4y=107-92} \\ \color{blue}{-32x+56x\underline{-28y+28y}=428-644} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3y=15 \\24x=-216\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{15}{-3}=-5 \\x=\frac{-216}{24}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-5)\}\)
  6. \(\left\{\begin{matrix}8x-8y=-40\\4y+7x=-57\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x-8y=-40\\7x+4y=-57\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-8y=-40& \color{red}{7.} & \color{blue}{1.} \\7x+4y=-57& \color{red}{-8.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{56x-56x}-56y-32y=-280+456} \\ \color{blue}{8x+14x\underline{-8y+8y}=-40-114} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-88y=176 \\22x=-154\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{176}{-88}=-2 \\x=\frac{-154}{22}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-2)\}\)
  7. \(\left\{\begin{matrix}4x-6y=66\\10x=-3y+75\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-6y=66\\10x+3y=75\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x-6y=66& \color{red}{5.} & \color{blue}{1.} \\10x+3y=75& \color{red}{-2.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}-30y-6y=330-150} \\ \color{blue}{4x+20x\underline{-6y+6y}=66+150} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-36y=180 \\24x=216\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{180}{-36}=-5 \\x=\frac{216}{24}=9\end{matrix}\right.\\ \qquad V=\{(9,-5)\}\)
  8. \(\left\{\begin{matrix}-10y=59-7x\\-5x+7y=-42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x-10y=59\\-5x+7y=-42\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-10y=59& \color{red}{5.} & \color{blue}{7.} \\-5x+7y=-42& \color{red}{7.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{35x-35x}-50y+49y=295-294} \\ \color{blue}{49x-50x\underline{-70y+70y}=413-420} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-y=1 \\-x=-7\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{1}{-1}=-1 \\x=\frac{-7}{-1}=7\end{matrix}\right.\\ \qquad V=\{(7,-1)\}\)
  9. \(\left\{\begin{matrix}8y=-80-3x\\-10x+3y=59\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+8y=-80\\-10x+3y=59\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+8y=-80& \color{red}{10.} & \color{blue}{3.} \\-10x+3y=59& \color{red}{3.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}+80y+9y=-800+177} \\ \color{blue}{9x+80x\underline{+24y-24y}=-240-472} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}89y=-623 \\89x=-712\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-623}{89}=-7 \\x=\frac{-712}{89}=-8\end{matrix}\right.\\ \qquad V=\{(-8,-7)\}\)
  10. \(\left\{\begin{matrix}-10x+6y=76\\-3y-9x=60\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x+6y=76\\-9x-3y=60\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x+6y=76& \color{red}{9.} & \color{blue}{1.} \\-9x-3y=60& \color{red}{-10.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-90x+90x}+54y+30y=684-600} \\ \color{blue}{-10x-18x\underline{+6y-6y}=76+120} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}84y=84 \\-28x=196\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{84}{84}=1 \\x=\frac{196}{-28}=-7\end{matrix}\right.\\ \qquad V=\{(-7,1)\}\)
  11. \(\left\{\begin{matrix}9x+9y=-54\\8x-3y=-26\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+9y=-54& \color{red}{8.} & \color{blue}{1.} \\8x-3y=-26& \color{red}{-9.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{72x-72x}+72y+27y=-432+234} \\ \color{blue}{9x+24x\underline{+9y-9y}=-54-78} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}99y=-198 \\33x=-132\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-198}{99}=-2 \\x=\frac{-132}{33}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-2)\}\)
  12. \(\left\{\begin{matrix}-9x+6y=18\\-6x+8y=-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+6y=18& \color{red}{2.} & \color{blue}{4.} \\-6x+8y=-12& \color{red}{-3.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}+12y-24y=36+36} \\ \color{blue}{-36x+18x\underline{+24y-24y}=72+36} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-12y=72 \\-18x=108\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{72}{-12}=-6 \\x=\frac{108}{-18}=-6\end{matrix}\right.\\ \qquad V=\{(-6,-6)\}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-17 09:54:26
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