Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}3y=9-3x\\7x-7y=7\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}2y+7x=-69\\-10x+5y=75\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}10y+2x=-50\\9x+9y=-81\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}6y-2x=-20\\-5x-7y=82\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}-4y=-90-9x\\7x-7y=-105\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-9y+7x=7\\4x-8y=24\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-10y=-128+8x\\-10x+4y=-28\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}2x-10y=82\\-5x+7y=-25\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}-5x-4y=4\\10x=-6y+4\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}4x+8y=8\\-4x+7y=-53\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}8y=-82-10x\\-3x-10y=17\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-5y+4x=5\\-5x+6y=-5\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}3y=9-3x\\7x-7y=7\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+3y=9\\7x-7y=7\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+3y=9& \color{red}{7.} & \color{blue}{7.} \\7x-7y=7& \color{red}{-3.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{21x-21x}+21y+21y=63-21} \\ \color{blue}{21x+21x\underline{+21y-21y}=63+21} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}42y=42 \\42x=84\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{42}{42}=1 \\x=\frac{84}{42}=2\end{matrix}\right.\\ \qquad V=\{(2,1)\}\)
  2. \(\left\{\begin{matrix}2y+7x=-69\\-10x+5y=75\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+2y=-69\\-10x+5y=75\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+2y=-69& \color{red}{10.} & \color{blue}{5.} \\-10x+5y=75& \color{red}{7.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{70x-70x}+20y+35y=-690+525} \\ \color{blue}{35x+20x\underline{+10y-10y}=-345-150} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}55y=-165 \\55x=-495\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-165}{55}=-3 \\x=\frac{-495}{55}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-3)\}\)
  3. \(\left\{\begin{matrix}10y+2x=-50\\9x+9y=-81\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+10y=-50\\9x+9y=-81\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+10y=-50& \color{red}{9.} & \color{blue}{9.} \\9x+9y=-81& \color{red}{-2.} & \color{blue}{-10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{18x-18x}+90y-18y=-450+162} \\ \color{blue}{18x-90x\underline{+90y-90y}=-450+810} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}72y=-288 \\-72x=360\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-288}{72}=-4 \\x=\frac{360}{-72}=-5\end{matrix}\right.\\ \qquad V=\{(-5,-4)\}\)
  4. \(\left\{\begin{matrix}6y-2x=-20\\-5x-7y=82\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+6y=-20\\-5x-7y=82\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+6y=-20& \color{red}{5.} & \color{blue}{7.} \\-5x-7y=82& \color{red}{-2.} & \color{blue}{6.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}+30y+14y=-100-164} \\ \color{blue}{-14x-30x\underline{+42y-42y}=-140+492} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}44y=-264 \\-44x=352\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-264}{44}=-6 \\x=\frac{352}{-44}=-8\end{matrix}\right.\\ \qquad V=\{(-8,-6)\}\)
  5. \(\left\{\begin{matrix}-4y=-90-9x\\7x-7y=-105\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x-4y=-90\\7x-7y=-105\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x-4y=-90& \color{red}{7.} & \color{blue}{7.} \\7x-7y=-105& \color{red}{-9.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{63x-63x}-28y+63y=-630+945} \\ \color{blue}{63x-28x\underline{-28y+28y}=-630+420} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}35y=315 \\35x=-210\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{315}{35}=9 \\x=\frac{-210}{35}=-6\end{matrix}\right.\\ \qquad V=\{(-6,9)\}\)
  6. \(\left\{\begin{matrix}-9y+7x=7\\4x-8y=24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x-9y=7\\4x-8y=24\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-9y=7& \color{red}{4.} & \color{blue}{8.} \\4x-8y=24& \color{red}{-7.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{28x-28x}-36y+56y=28-168} \\ \color{blue}{56x-36x\underline{-72y+72y}=56-216} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}20y=-140 \\20x=-160\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-140}{20}=-7 \\x=\frac{-160}{20}=-8\end{matrix}\right.\\ \qquad V=\{(-8,-7)\}\)
  7. \(\left\{\begin{matrix}-10y=-128+8x\\-10x+4y=-28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-10y=-128\\-10x+4y=-28\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-10y=-128& \color{red}{5.} & \color{blue}{2.} \\-10x+4y=-28& \color{red}{-4.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-40x+40x}-50y-16y=-640+112} \\ \color{blue}{-16x-50x\underline{-20y+20y}=-256-140} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-66y=-528 \\-66x=-396\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-528}{-66}=8 \\x=\frac{-396}{-66}=6\end{matrix}\right.\\ \qquad V=\{(6,8)\}\)
  8. \(\left\{\begin{matrix}2x-10y=82\\-5x+7y=-25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x-10y=82& \color{red}{5.} & \color{blue}{7.} \\-5x+7y=-25& \color{red}{2.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-50y+14y=410-50} \\ \color{blue}{14x-50x\underline{-70y+70y}=574-250} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-36y=360 \\-36x=324\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{360}{-36}=-10 \\x=\frac{324}{-36}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-10)\}\)
  9. \(\left\{\begin{matrix}-5x-4y=4\\10x=-6y+4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-4y=4\\10x+6y=4\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-4y=4& \color{red}{2.} & \color{blue}{3.} \\10x+6y=4& \color{red}{1.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}-8y+6y=8+4} \\ \color{blue}{-15x+20x\underline{-12y+12y}=12+8} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2y=12 \\5x=20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{12}{-2}=-6 \\x=\frac{20}{5}=4\end{matrix}\right.\\ \qquad V=\{(4,-6)\}\)
  10. \(\left\{\begin{matrix}4x+8y=8\\-4x+7y=-53\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+8y=8& \color{red}{1.} & \color{blue}{7.} \\-4x+7y=-53& \color{red}{1.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{4x-4x}+8y+7y=8-53} \\ \color{blue}{28x+32x\underline{+56y-56y}=56+424} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}15y=-45 \\60x=480\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-45}{15}=-3 \\x=\frac{480}{60}=8\end{matrix}\right.\\ \qquad V=\{(8,-3)\}\)
  11. \(\left\{\begin{matrix}8y=-82-10x\\-3x-10y=17\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x+8y=-82\\-3x-10y=17\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x+8y=-82& \color{red}{3.} & \color{blue}{5.} \\-3x-10y=17& \color{red}{10.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}+24y-100y=-246+170} \\ \color{blue}{50x-12x\underline{+40y-40y}=-410+68} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-76y=-76 \\38x=-342\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-76}{-76}=1 \\x=\frac{-342}{38}=-9\end{matrix}\right.\\ \qquad V=\{(-9,1)\}\)
  12. \(\left\{\begin{matrix}-5y+4x=5\\-5x+6y=-5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-5y=5\\-5x+6y=-5\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x-5y=5& \color{red}{5.} & \color{blue}{6.} \\-5x+6y=-5& \color{red}{4.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}-25y+24y=25-20} \\ \color{blue}{24x-25x\underline{-30y+30y}=30-25} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-y=5 \\-x=5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{5}{-1}=-5 \\x=\frac{5}{-1}=-5\end{matrix}\right.\\ \qquad V=\{(-5,-5)\}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-03-07 03:30:55