Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}6y+2x=20\\-8x+5y=-51\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}-8x+6y=90\\-2x=5y+3\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}6x-3y=33\\-5x-7y=58\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}8y=-28-4x\\3x+9y=-30\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}7y=-24-2x\\-10x+3y=-32\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}10x+3y=2\\-10y+9x=-49\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-10x-8y=8\\6x=6y-102\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-8x-5y=6\\-10y-9x=-37\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}9x+3y=72\\-6x=5y-57\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-2y=-58+6x\\-10x-4y=-98\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}3y=29+5x\\5x+2y=-39\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-9y-2x=3\\9x-4y=31\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}6y+2x=20\\-8x+5y=-51\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+6y=20\\-8x+5y=-51\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+6y=20& \color{red}{4.} & \color{blue}{5.} \\-8x+5y=-51& \color{red}{1.} & \color{blue}{-6.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}+24y+5y=80-51} \\ \color{blue}{10x+48x\underline{+30y-30y}=100+306} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}29y=29 \\58x=406\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{29}{29}=1 \\x=\frac{406}{58}=7\end{matrix}\right.\\ \qquad V=\{(7,1)\}\)
  2. \(\left\{\begin{matrix}-8x+6y=90\\-2x=5y+3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+6y=90\\-2x-5y=3\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+6y=90& \color{red}{1.} & \color{blue}{5.} \\-2x-5y=3& \color{red}{-4.} & \color{blue}{6.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}+6y+20y=90-12} \\ \color{blue}{-40x-12x\underline{+30y-30y}=450+18} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}26y=78 \\-52x=468\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{78}{26}=3 \\x=\frac{468}{-52}=-9\end{matrix}\right.\\ \qquad V=\{(-9,3)\}\)
  3. \(\left\{\begin{matrix}6x-3y=33\\-5x-7y=58\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-3y=33& \color{red}{5.} & \color{blue}{7.} \\-5x-7y=58& \color{red}{6.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}-15y-42y=165+348} \\ \color{blue}{42x+15x\underline{-21y+21y}=231-174} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-57y=513 \\57x=57\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{513}{-57}=-9 \\x=\frac{57}{57}=1\end{matrix}\right.\\ \qquad V=\{(1,-9)\}\)
  4. \(\left\{\begin{matrix}8y=-28-4x\\3x+9y=-30\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+8y=-28\\3x+9y=-30\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+8y=-28& \color{red}{3.} & \color{blue}{9.} \\3x+9y=-30& \color{red}{-4.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{12x-12x}+24y-36y=-84+120} \\ \color{blue}{36x-24x\underline{+72y-72y}=-252+240} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-12y=36 \\12x=-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{36}{-12}=-3 \\x=\frac{-12}{12}=-1\end{matrix}\right.\\ \qquad V=\{(-1,-3)\}\)
  5. \(\left\{\begin{matrix}7y=-24-2x\\-10x+3y=-32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+7y=-24\\-10x+3y=-32\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+7y=-24& \color{red}{5.} & \color{blue}{3.} \\-10x+3y=-32& \color{red}{1.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}+35y+3y=-120-32} \\ \color{blue}{6x+70x\underline{+21y-21y}=-72+224} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}38y=-152 \\76x=152\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-152}{38}=-4 \\x=\frac{152}{76}=2\end{matrix}\right.\\ \qquad V=\{(2,-4)\}\)
  6. \(\left\{\begin{matrix}10x+3y=2\\-10y+9x=-49\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x+3y=2\\9x-10y=-49\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x+3y=2& \color{red}{9.} & \color{blue}{10.} \\9x-10y=-49& \color{red}{-10.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{90x-90x}+27y+100y=18+490} \\ \color{blue}{100x+27x\underline{+30y-30y}=20-147} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}127y=508 \\127x=-127\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{508}{127}=4 \\x=\frac{-127}{127}=-1\end{matrix}\right.\\ \qquad V=\{(-1,4)\}\)
  7. \(\left\{\begin{matrix}-10x-8y=8\\6x=6y-102\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x-8y=8\\6x-6y=-102\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x-8y=8& \color{red}{3.} & \color{blue}{3.} \\6x-6y=-102& \color{red}{5.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}-24y-30y=24-510} \\ \color{blue}{-30x-24x\underline{-24y+24y}=24+408} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-54y=-486 \\-54x=432\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-486}{-54}=9 \\x=\frac{432}{-54}=-8\end{matrix}\right.\\ \qquad V=\{(-8,9)\}\)
  8. \(\left\{\begin{matrix}-8x-5y=6\\-10y-9x=-37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-5y=6\\-9x-10y=-37\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-5y=6& \color{red}{9.} & \color{blue}{2.} \\-9x-10y=-37& \color{red}{-8.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-72x+72x}-45y+80y=54+296} \\ \color{blue}{-16x+9x\underline{-10y+10y}=12+37} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}35y=350 \\-7x=49\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{350}{35}=10 \\x=\frac{49}{-7}=-7\end{matrix}\right.\\ \qquad V=\{(-7,10)\}\)
  9. \(\left\{\begin{matrix}9x+3y=72\\-6x=5y-57\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x+3y=72\\-6x-5y=-57\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+3y=72& \color{red}{2.} & \color{blue}{5.} \\-6x-5y=-57& \color{red}{3.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{18x-18x}+6y-15y=144-171} \\ \color{blue}{45x-18x\underline{+15y-15y}=360-171} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9y=-27 \\27x=189\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-27}{-9}=3 \\x=\frac{189}{27}=7\end{matrix}\right.\\ \qquad V=\{(7,3)\}\)
  10. \(\left\{\begin{matrix}-2y=-58+6x\\-10x-4y=-98\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x-2y=-58\\-10x-4y=-98\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-2y=-58& \color{red}{5.} & \color{blue}{2.} \\-10x-4y=-98& \color{red}{-3.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}-10y+12y=-290+294} \\ \color{blue}{-12x+10x\underline{-4y+4y}=-116+98} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2y=4 \\-2x=-18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{4}{2}=2 \\x=\frac{-18}{-2}=9\end{matrix}\right.\\ \qquad V=\{(9,2)\}\)
  11. \(\left\{\begin{matrix}3y=29+5x\\5x+2y=-39\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+3y=29\\5x+2y=-39\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x+3y=29& \color{red}{1.} & \color{blue}{2.} \\5x+2y=-39& \color{red}{1.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-5x+5x}+3y+2y=29-39} \\ \color{blue}{-10x-15x\underline{+6y-6y}=58+117} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5y=-10 \\-25x=175\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-10}{5}=-2 \\x=\frac{175}{-25}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-2)\}\)
  12. \(\left\{\begin{matrix}-9y-2x=3\\9x-4y=31\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-9y=3\\9x-4y=31\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x-9y=3& \color{red}{9.} & \color{blue}{4.} \\9x-4y=31& \color{red}{2.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}-81y-8y=27+62} \\ \color{blue}{-8x-81x\underline{-36y+36y}=12-279} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-89y=89 \\-89x=-267\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{89}{-89}=-1 \\x=\frac{-267}{-89}=3\end{matrix}\right.\\ \qquad V=\{(3,-1)\}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-02 03:29:35
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