Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}7x+4y=-31\\4x=8y-100\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}8x+7y=42\\6x-10y=62\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}4y=-18-3x\\10x-8y=132\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-7y=25+2x\\-3x+2y=0\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}6x-6y=54\\8y+7x=18\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-7y=63+7x\\6x+9y=-60\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}5x-3y=10\\9x-2y=52\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}10y=48-6x\\4x+4y=16\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}7x+7y=-91\\-4x=9y+72\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}8x-6y=48\\-8x-7y=4\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}-2x-2y=20\\8y-8x=32\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-6x-6y=18\\8x-4y=-84\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}7x+4y=-31\\4x=8y-100\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+4y=-31\\4x-8y=-100\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+4y=-31& \color{red}{4.} & \color{blue}{2.} \\4x-8y=-100& \color{red}{-7.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{28x-28x}+16y+56y=-124+700} \\ \color{blue}{14x+4x\underline{+8y-8y}=-62-100} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}72y=576 \\18x=-162\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{576}{72}=8 \\x=\frac{-162}{18}=-9\end{matrix}\right.\\ \qquad V=\{(-9,8)\}\)
  2. \(\left\{\begin{matrix}8x+7y=42\\6x-10y=62\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+7y=42& \color{red}{3.} & \color{blue}{10.} \\6x-10y=62& \color{red}{-4.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{24x-24x}+21y+40y=126-248} \\ \color{blue}{80x+42x\underline{+70y-70y}=420+434} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}61y=-122 \\122x=854\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-122}{61}=-2 \\x=\frac{854}{122}=7\end{matrix}\right.\\ \qquad V=\{(7,-2)\}\)
  3. \(\left\{\begin{matrix}4y=-18-3x\\10x-8y=132\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+4y=-18\\10x-8y=132\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+4y=-18& \color{red}{10.} & \color{blue}{2.} \\10x-8y=132& \color{red}{-3.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}+40y+24y=-180-396} \\ \color{blue}{6x+10x\underline{+8y-8y}=-36+132} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}64y=-576 \\16x=96\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-576}{64}=-9 \\x=\frac{96}{16}=6\end{matrix}\right.\\ \qquad V=\{(6,-9)\}\)
  4. \(\left\{\begin{matrix}-7y=25+2x\\-3x+2y=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-7y=25\\-3x+2y=0\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x-7y=25& \color{red}{3.} & \color{blue}{2.} \\-3x+2y=0& \color{red}{-2.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}-21y-4y=75+0} \\ \color{blue}{-4x-21x\underline{-14y+14y}=50+0} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-25y=75 \\-25x=50\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{75}{-25}=-3 \\x=\frac{50}{-25}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-3)\}\)
  5. \(\left\{\begin{matrix}6x-6y=54\\8y+7x=18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x-6y=54\\7x+8y=18\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-6y=54& \color{red}{7.} & \color{blue}{4.} \\7x+8y=18& \color{red}{-6.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{42x-42x}-42y-48y=378-108} \\ \color{blue}{24x+21x\underline{-24y+24y}=216+54} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-90y=270 \\45x=270\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{270}{-90}=-3 \\x=\frac{270}{45}=6\end{matrix}\right.\\ \qquad V=\{(6,-3)\}\)
  6. \(\left\{\begin{matrix}-7y=63+7x\\6x+9y=-60\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-7y=63\\6x+9y=-60\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-7y=63& \color{red}{6.} & \color{blue}{9.} \\6x+9y=-60& \color{red}{7.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-42x+42x}-42y+63y=378-420} \\ \color{blue}{-63x+42x\underline{-63y+63y}=567-420} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}21y=-42 \\-21x=147\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-42}{21}=-2 \\x=\frac{147}{-21}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-2)\}\)
  7. \(\left\{\begin{matrix}5x-3y=10\\9x-2y=52\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-3y=10& \color{red}{9.} & \color{blue}{2.} \\9x-2y=52& \color{red}{-5.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{45x-45x}-27y+10y=90-260} \\ \color{blue}{10x-27x\underline{-6y+6y}=20-156} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-17y=-170 \\-17x=-136\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-170}{-17}=10 \\x=\frac{-136}{-17}=8\end{matrix}\right.\\ \qquad V=\{(8,10)\}\)
  8. \(\left\{\begin{matrix}10y=48-6x\\4x+4y=16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+10y=48\\4x+4y=16\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x+10y=48& \color{red}{2.} & \color{blue}{2.} \\4x+4y=16& \color{red}{-3.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{12x-12x}+20y-12y=96-48} \\ \color{blue}{12x-20x\underline{+20y-20y}=96-80} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8y=48 \\-8x=16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{48}{8}=6 \\x=\frac{16}{-8}=-2\end{matrix}\right.\\ \qquad V=\{(-2,6)\}\)
  9. \(\left\{\begin{matrix}7x+7y=-91\\-4x=9y+72\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+7y=-91\\-4x-9y=72\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+7y=-91& \color{red}{4.} & \color{blue}{9.} \\-4x-9y=72& \color{red}{7.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{28x-28x}+28y-63y=-364+504} \\ \color{blue}{63x-28x\underline{+63y-63y}=-819+504} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-35y=140 \\35x=-315\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{140}{-35}=-4 \\x=\frac{-315}{35}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-4)\}\)
  10. \(\left\{\begin{matrix}8x-6y=48\\-8x-7y=4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-6y=48& \color{red}{1.} & \color{blue}{7.} \\-8x-7y=4& \color{red}{1.} & \color{blue}{-6.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}-6y-7y=48+4} \\ \color{blue}{56x+48x\underline{-42y+42y}=336-24} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-13y=52 \\104x=312\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{52}{-13}=-4 \\x=\frac{312}{104}=3\end{matrix}\right.\\ \qquad V=\{(3,-4)\}\)
  11. \(\left\{\begin{matrix}-2x-2y=20\\8y-8x=32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-2y=20\\-8x+8y=32\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x-2y=20& \color{red}{4.} & \color{blue}{4.} \\-8x+8y=32& \color{red}{-1.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}-8y-8y=80-32} \\ \color{blue}{-8x-8x\underline{-8y+8y}=80+32} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-16y=48 \\-16x=112\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{48}{-16}=-3 \\x=\frac{112}{-16}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-3)\}\)
  12. \(\left\{\begin{matrix}-6x-6y=18\\8x-4y=-84\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-6y=18& \color{red}{4.} & \color{blue}{2.} \\8x-4y=-84& \color{red}{3.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}-24y-12y=72-252} \\ \color{blue}{-12x-24x\underline{-12y+12y}=36+252} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-36y=-180 \\-36x=288\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-180}{-36}=5 \\x=\frac{288}{-36}=-8\end{matrix}\right.\\ \qquad V=\{(-8,5)\}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-14 01:44:25
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