Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}-7x-2y=-33\\6x+8y=66\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}2x-8y=20\\-2x=-10y-26\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}2y=-40+6x\\9x+6y=69\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-7x-5y=-46\\-8x=-6y+6\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}10x-7y=76\\10x-9y=92\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-4y=-44-4x\\3x+5y=-17\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}9y=0+9x\\-9x-2y=11\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}6x+8y=30\\-2x=4y-14\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}-4y=-42-9x\\8x+3y=2\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}7y=5+9x\\9x-6y=-3\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}-2x-3y=39\\-5y-8x=107\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-7y=-3+10x\\-6x-8y=-36\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}-7x-2y=-33\\6x+8y=66\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-2y=-33& \color{red}{6.} & \color{blue}{4.} \\6x+8y=66& \color{red}{7.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-42x+42x}-12y+56y=-198+462} \\ \color{blue}{-28x+6x\underline{-8y+8y}=-132+66} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}44y=264 \\-22x=-66\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{264}{44}=6 \\x=\frac{-66}{-22}=3\end{matrix}\right.\\ \qquad V=\{(3,6)\}\)
  2. \(\left\{\begin{matrix}2x-8y=20\\-2x=-10y-26\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x-8y=20\\-2x+10y=-26\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x-8y=20& \color{red}{1.} & \color{blue}{5.} \\-2x+10y=-26& \color{red}{1.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{2x-2x}-8y+10y=20-26} \\ \color{blue}{10x-8x\underline{-40y+40y}=100-104} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2y=-6 \\2x=-4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-6}{2}=-3 \\x=\frac{-4}{2}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-3)\}\)
  3. \(\left\{\begin{matrix}2y=-40+6x\\9x+6y=69\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+2y=-40\\9x+6y=69\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+2y=-40& \color{red}{3.} & \color{blue}{3.} \\9x+6y=69& \color{red}{2.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}+6y+12y=-120+138} \\ \color{blue}{-18x-9x\underline{+6y-6y}=-120-69} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}18y=18 \\-27x=-189\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{18}{18}=1 \\x=\frac{-189}{-27}=7\end{matrix}\right.\\ \qquad V=\{(7,1)\}\)
  4. \(\left\{\begin{matrix}-7x-5y=-46\\-8x=-6y+6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-5y=-46\\-8x+6y=6\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-5y=-46& \color{red}{8.} & \color{blue}{6.} \\-8x+6y=6& \color{red}{-7.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-56x+56x}-40y-42y=-368-42} \\ \color{blue}{-42x-40x\underline{-30y+30y}=-276+30} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-82y=-410 \\-82x=-246\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-410}{-82}=5 \\x=\frac{-246}{-82}=3\end{matrix}\right.\\ \qquad V=\{(3,5)\}\)
  5. \(\left\{\begin{matrix}10x-7y=76\\10x-9y=92\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-7y=76& \color{red}{1.} & \color{blue}{9.} \\10x-9y=92& \color{red}{-1.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-7y+9y=76-92} \\ \color{blue}{90x-70x\underline{-63y+63y}=684-644} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2y=-16 \\20x=40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-16}{2}=-8 \\x=\frac{40}{20}=2\end{matrix}\right.\\ \qquad V=\{(2,-8)\}\)
  6. \(\left\{\begin{matrix}-4y=-44-4x\\3x+5y=-17\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-4y=-44\\3x+5y=-17\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x-4y=-44& \color{red}{3.} & \color{blue}{5.} \\3x+5y=-17& \color{red}{-4.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{12x-12x}-12y-20y=-132+68} \\ \color{blue}{20x+12x\underline{-20y+20y}=-220-68} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-32y=-64 \\32x=-288\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-64}{-32}=2 \\x=\frac{-288}{32}=-9\end{matrix}\right.\\ \qquad V=\{(-9,2)\}\)
  7. \(\left\{\begin{matrix}9y=0+9x\\-9x-2y=11\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x+9y=0\\-9x-2y=11\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+9y=0& \color{red}{1.} & \color{blue}{2.} \\-9x-2y=11& \color{red}{-1.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-9x+9x}+9y+2y=0-11} \\ \color{blue}{-18x-81x\underline{+18y-18y}=0+99} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}11y=-11 \\-99x=99\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-11}{11}=-1 \\x=\frac{99}{-99}=-1\end{matrix}\right.\\ \qquad V=\{(-1,-1)\}\)
  8. \(\left\{\begin{matrix}6x+8y=30\\-2x=4y-14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+8y=30\\-2x-4y=-14\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x+8y=30& \color{red}{1.} & \color{blue}{1.} \\-2x-4y=-14& \color{red}{3.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}+8y-12y=30-42} \\ \color{blue}{6x-4x\underline{+8y-8y}=30-28} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4y=-12 \\2x=2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-12}{-4}=3 \\x=\frac{2}{2}=1\end{matrix}\right.\\ \qquad V=\{(1,3)\}\)
  9. \(\left\{\begin{matrix}-4y=-42-9x\\8x+3y=2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x-4y=-42\\8x+3y=2\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x-4y=-42& \color{red}{8.} & \color{blue}{3.} \\8x+3y=2& \color{red}{-9.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{72x-72x}-32y-27y=-336-18} \\ \color{blue}{27x+32x\underline{-12y+12y}=-126+8} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-59y=-354 \\59x=-118\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-354}{-59}=6 \\x=\frac{-118}{59}=-2\end{matrix}\right.\\ \qquad V=\{(-2,6)\}\)
  10. \(\left\{\begin{matrix}7y=5+9x\\9x-6y=-3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x+7y=5\\9x-6y=-3\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+7y=5& \color{red}{1.} & \color{blue}{6.} \\9x-6y=-3& \color{red}{1.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-9x+9x}+7y-6y=5-3} \\ \color{blue}{-54x+63x\underline{+42y-42y}=30-21} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=2 \\9x=9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{2}{1}=2 \\x=\frac{9}{9}=1\end{matrix}\right.\\ \qquad V=\{(1,2)\}\)
  11. \(\left\{\begin{matrix}-2x-3y=39\\-5y-8x=107\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-3y=39\\-8x-5y=107\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x-3y=39& \color{red}{4.} & \color{blue}{5.} \\-8x-5y=107& \color{red}{-1.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}-12y+5y=156-107} \\ \color{blue}{-10x+24x\underline{-15y+15y}=195-321} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7y=49 \\14x=-126\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{49}{-7}=-7 \\x=\frac{-126}{14}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-7)\}\)
  12. \(\left\{\begin{matrix}-7y=-3+10x\\-6x-8y=-36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x-7y=-3\\-6x-8y=-36\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x-7y=-3& \color{red}{3.} & \color{blue}{8.} \\-6x-8y=-36& \color{red}{-5.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}-21y+40y=-9+180} \\ \color{blue}{-80x+42x\underline{-56y+56y}=-24+252} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}19y=171 \\-38x=228\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{171}{19}=9 \\x=\frac{228}{-38}=-6\end{matrix}\right.\\ \qquad V=\{(-6,9)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-04-04 04:55:53