Stelsels combinatie

Hoofdmenu Eentje per keer 

Combinatie

  1. \(\left\{\begin{matrix}-3x+2y=18\\10y-10x=70\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}3y=-15+3x\\-7x+7y=-35\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}-8x+7y=-91\\-8y+2x=54\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-7x-6y=81\\8y+2x=-42\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-5x-5y=-85\\-8y+9x=17\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}6x+5y=49\\-2y-8x=-42\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}3y=2-4x\\5x-7y=-62\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}3x+9y=42\\-8y+5x=-114\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}-3y=-3+3x\\9x+5y=37\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-6y-10x=-18\\-7x-8y=-43\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}2x+7y=51\\6x=-10y+76\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-5x-8y=17\\2x+7y=-3\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}-3x+2y=18\\10y-10x=70\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+2y=18\\-10x+10y=70\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+2y=18& \color{red}{10.} & \color{blue}{5.} \\-10x+10y=70& \color{red}{-3.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}+20y-30y=180-210} \\ \color{blue}{-15x+10x\underline{+10y-10y}=90-70} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10y=-30 \\-5x=20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-30}{-10}=3 \\x=\frac{20}{-5}=-4\end{matrix}\right.\\ \qquad V=\{(-4,3)\}\)
  2. \(\left\{\begin{matrix}3y=-15+3x\\-7x+7y=-35\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+3y=-15\\-7x+7y=-35\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+3y=-15& \color{red}{7.} & \color{blue}{7.} \\-7x+7y=-35& \color{red}{-3.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-21x+21x}+21y-21y=-105+105} \\ \color{blue}{-21x+21x\underline{+21y-21y}=-105+105} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}0y=0 \\0x=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{0}{0}=-7 \\x=\frac{0}{0}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-7)\}\)
  3. \(\left\{\begin{matrix}-8x+7y=-91\\-8y+2x=54\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+7y=-91\\2x-8y=54\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+7y=-91& \color{red}{1.} & \color{blue}{8.} \\2x-8y=54& \color{red}{4.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}+7y-32y=-91+216} \\ \color{blue}{-64x+14x\underline{+56y-56y}=-728+378} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-25y=125 \\-50x=-350\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{125}{-25}=-5 \\x=\frac{-350}{-50}=7\end{matrix}\right.\\ \qquad V=\{(7,-5)\}\)
  4. \(\left\{\begin{matrix}-7x-6y=81\\8y+2x=-42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-6y=81\\2x+8y=-42\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-6y=81& \color{red}{2.} & \color{blue}{4.} \\2x+8y=-42& \color{red}{7.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-14x+14x}-12y+56y=162-294} \\ \color{blue}{-28x+6x\underline{-24y+24y}=324-126} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}44y=-132 \\-22x=198\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-132}{44}=-3 \\x=\frac{198}{-22}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-3)\}\)
  5. \(\left\{\begin{matrix}-5x-5y=-85\\-8y+9x=17\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-5y=-85\\9x-8y=17\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-5y=-85& \color{red}{9.} & \color{blue}{8.} \\9x-8y=17& \color{red}{5.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-45x+45x}-45y-40y=-765+85} \\ \color{blue}{-40x-45x\underline{-40y+40y}=-680-85} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-85y=-680 \\-85x=-765\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-680}{-85}=8 \\x=\frac{-765}{-85}=9\end{matrix}\right.\\ \qquad V=\{(9,8)\}\)
  6. \(\left\{\begin{matrix}6x+5y=49\\-2y-8x=-42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+5y=49\\-8x-2y=-42\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x+5y=49& \color{red}{4.} & \color{blue}{2.} \\-8x-2y=-42& \color{red}{3.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{24x-24x}+20y-6y=196-126} \\ \color{blue}{12x-40x\underline{+10y-10y}=98-210} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}14y=70 \\-28x=-112\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{70}{14}=5 \\x=\frac{-112}{-28}=4\end{matrix}\right.\\ \qquad V=\{(4,5)\}\)
  7. \(\left\{\begin{matrix}3y=2-4x\\5x-7y=-62\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+3y=2\\5x-7y=-62\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+3y=2& \color{red}{5.} & \color{blue}{7.} \\5x-7y=-62& \color{red}{-4.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}+15y+28y=10+248} \\ \color{blue}{28x+15x\underline{+21y-21y}=14-186} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}43y=258 \\43x=-172\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{258}{43}=6 \\x=\frac{-172}{43}=-4\end{matrix}\right.\\ \qquad V=\{(-4,6)\}\)
  8. \(\left\{\begin{matrix}3x+9y=42\\-8y+5x=-114\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+9y=42\\5x-8y=-114\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+9y=42& \color{red}{5.} & \color{blue}{8.} \\5x-8y=-114& \color{red}{-3.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{15x-15x}+45y+24y=210+342} \\ \color{blue}{24x+45x\underline{+72y-72y}=336-1026} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}69y=552 \\69x=-690\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{552}{69}=8 \\x=\frac{-690}{69}=-10\end{matrix}\right.\\ \qquad V=\{(-10,8)\}\)
  9. \(\left\{\begin{matrix}-3y=-3+3x\\9x+5y=37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x-3y=-3\\9x+5y=37\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x-3y=-3& \color{red}{3.} & \color{blue}{5.} \\9x+5y=37& \color{red}{1.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-9x+9x}-9y+5y=-9+37} \\ \color{blue}{-15x+27x\underline{-15y+15y}=-15+111} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4y=28 \\12x=96\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{28}{-4}=-7 \\x=\frac{96}{12}=8\end{matrix}\right.\\ \qquad V=\{(8,-7)\}\)
  10. \(\left\{\begin{matrix}-6y-10x=-18\\-7x-8y=-43\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x-6y=-18\\-7x-8y=-43\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x-6y=-18& \color{red}{7.} & \color{blue}{4.} \\-7x-8y=-43& \color{red}{-10.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-70x+70x}-42y+80y=-126+430} \\ \color{blue}{-40x+21x\underline{-24y+24y}=-72+129} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}38y=304 \\-19x=57\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{304}{38}=8 \\x=\frac{57}{-19}=-3\end{matrix}\right.\\ \qquad V=\{(-3,8)\}\)
  11. \(\left\{\begin{matrix}2x+7y=51\\6x=-10y+76\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+7y=51\\6x+10y=76\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+7y=51& \color{red}{3.} & \color{blue}{10.} \\6x+10y=76& \color{red}{-1.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}+21y-10y=153-76} \\ \color{blue}{20x-42x\underline{+70y-70y}=510-532} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}11y=77 \\-22x=-22\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{77}{11}=7 \\x=\frac{-22}{-22}=1\end{matrix}\right.\\ \qquad V=\{(1,7)\}\)
  12. \(\left\{\begin{matrix}-5x-8y=17\\2x+7y=-3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-8y=17& \color{red}{2.} & \color{blue}{7.} \\2x+7y=-3& \color{red}{5.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}-16y+35y=34-15} \\ \color{blue}{-35x+16x\underline{-56y+56y}=119-24} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}19y=19 \\-19x=95\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{19}{19}=1 \\x=\frac{95}{-19}=-5\end{matrix}\right.\\ \qquad V=\{(-5,1)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-14 00:17:04