Stelsels combinatie

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Combinatie

  1. \(\left\{\begin{matrix}-6y+7x=70\\10x-2y=54\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}5x-3y=-47\\3x=-10y+78\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}-5x-5y=40\\-10y+2x=-4\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}-2y=47-3x\\-5x-8y=35\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}6x-2y=-6\\-10x+7y=-23\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}6y+2x=-2\\5x-9y=-77\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-10y-2x=12\\-8x-8y=-48\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-7y=-43-3x\\8x-10y=-54\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}8y-8x=-112\\-2x+5y=-46\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}8x+4y=32\\10x=5y+120\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}-9y-4x=78\\9x+6y=-90\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}-2y+10x=44\\-4x+6y=24\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}-6y+7x=70\\10x-2y=54\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x-6y=70\\10x-2y=54\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-6y=70& \color{red}{10.} & \color{blue}{1.} \\10x-2y=54& \color{red}{-7.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{70x-70x}-60y+14y=700-378} \\ \color{blue}{7x-30x\underline{-6y+6y}=70-162} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-46y=322 \\-23x=-92\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{322}{-46}=-7 \\x=\frac{-92}{-23}=4\end{matrix}\right.\\ \qquad V=\{(4,-7)\}\)
  2. \(\left\{\begin{matrix}5x-3y=-47\\3x=-10y+78\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-3y=-47\\3x+10y=78\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-3y=-47& \color{red}{3.} & \color{blue}{10.} \\3x+10y=78& \color{red}{-5.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{15x-15x}-9y-50y=-141-390} \\ \color{blue}{50x+9x\underline{-30y+30y}=-470+234} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-59y=-531 \\59x=-236\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-531}{-59}=9 \\x=\frac{-236}{59}=-4\end{matrix}\right.\\ \qquad V=\{(-4,9)\}\)
  3. \(\left\{\begin{matrix}-5x-5y=40\\-10y+2x=-4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-5y=40\\2x-10y=-4\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-5y=40& \color{red}{2.} & \color{blue}{2.} \\2x-10y=-4& \color{red}{5.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}-10y-50y=80-20} \\ \color{blue}{-10x-2x\underline{-10y+10y}=80+4} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-60y=60 \\-12x=84\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{60}{-60}=-1 \\x=\frac{84}{-12}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-1)\}\)
  4. \(\left\{\begin{matrix}-2y=47-3x\\-5x-8y=35\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-2y=47\\-5x-8y=35\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-2y=47& \color{red}{5.} & \color{blue}{4.} \\-5x-8y=35& \color{red}{3.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{15x-15x}-10y-24y=235+105} \\ \color{blue}{12x+5x\underline{-8y+8y}=188-35} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-34y=340 \\17x=153\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{340}{-34}=-10 \\x=\frac{153}{17}=9\end{matrix}\right.\\ \qquad V=\{(9,-10)\}\)
  5. \(\left\{\begin{matrix}6x-2y=-6\\-10x+7y=-23\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-2y=-6& \color{red}{5.} & \color{blue}{7.} \\-10x+7y=-23& \color{red}{3.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}-10y+21y=-30-69} \\ \color{blue}{42x-20x\underline{-14y+14y}=-42-46} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}11y=-99 \\22x=-88\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-99}{11}=-9 \\x=\frac{-88}{22}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-9)\}\)
  6. \(\left\{\begin{matrix}6y+2x=-2\\5x-9y=-77\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+6y=-2\\5x-9y=-77\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+6y=-2& \color{red}{5.} & \color{blue}{3.} \\5x-9y=-77& \color{red}{-2.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}+30y+18y=-10+154} \\ \color{blue}{6x+10x\underline{+18y-18y}=-6-154} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}48y=144 \\16x=-160\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{144}{48}=3 \\x=\frac{-160}{16}=-10\end{matrix}\right.\\ \qquad V=\{(-10,3)\}\)
  7. \(\left\{\begin{matrix}-10y-2x=12\\-8x-8y=-48\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-10y=12\\-8x-8y=-48\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x-10y=12& \color{red}{4.} & \color{blue}{4.} \\-8x-8y=-48& \color{red}{-1.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}-40y+8y=48+48} \\ \color{blue}{-8x+40x\underline{-40y+40y}=48+240} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-32y=96 \\32x=288\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{96}{-32}=-3 \\x=\frac{288}{32}=9\end{matrix}\right.\\ \qquad V=\{(9,-3)\}\)
  8. \(\left\{\begin{matrix}-7y=-43-3x\\8x-10y=-54\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-7y=-43\\8x-10y=-54\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-7y=-43& \color{red}{8.} & \color{blue}{10.} \\8x-10y=-54& \color{red}{-3.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{24x-24x}-56y+30y=-344+162} \\ \color{blue}{30x-56x\underline{-70y+70y}=-430+378} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-26y=-182 \\-26x=-52\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-182}{-26}=7 \\x=\frac{-52}{-26}=2\end{matrix}\right.\\ \qquad V=\{(2,7)\}\)
  9. \(\left\{\begin{matrix}8y-8x=-112\\-2x+5y=-46\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+8y=-112\\-2x+5y=-46\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+8y=-112& \color{red}{1.} & \color{blue}{5.} \\-2x+5y=-46& \color{red}{-4.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}+8y-20y=-112+184} \\ \color{blue}{-40x+16x\underline{+40y-40y}=-560+368} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-12y=72 \\-24x=-192\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{72}{-12}=-6 \\x=\frac{-192}{-24}=8\end{matrix}\right.\\ \qquad V=\{(8,-6)\}\)
  10. \(\left\{\begin{matrix}8x+4y=32\\10x=5y+120\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x+4y=32\\10x-5y=120\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+4y=32& \color{red}{5.} & \color{blue}{5.} \\10x-5y=120& \color{red}{-4.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}+20y+20y=160-480} \\ \color{blue}{40x+40x\underline{+20y-20y}=160+480} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}40y=-320 \\80x=640\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-320}{40}=-8 \\x=\frac{640}{80}=8\end{matrix}\right.\\ \qquad V=\{(8,-8)\}\)
  11. \(\left\{\begin{matrix}-9y-4x=78\\9x+6y=-90\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-9y=78\\9x+6y=-90\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x-9y=78& \color{red}{9.} & \color{blue}{2.} \\9x+6y=-90& \color{red}{4.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-36x+36x}-81y+24y=702-360} \\ \color{blue}{-8x+27x\underline{-18y+18y}=156-270} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-57y=342 \\19x=-114\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{342}{-57}=-6 \\x=\frac{-114}{19}=-6\end{matrix}\right.\\ \qquad V=\{(-6,-6)\}\)
  12. \(\left\{\begin{matrix}-2y+10x=44\\-4x+6y=24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x-2y=44\\-4x+6y=24\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-2y=44& \color{red}{2.} & \color{blue}{3.} \\-4x+6y=24& \color{red}{5.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}-4y+30y=88+120} \\ \color{blue}{30x-4x\underline{-6y+6y}=132+24} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}26y=208 \\26x=156\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{208}{26}=8 \\x=\frac{156}{26}=6\end{matrix}\right.\\ \qquad V=\{(6,8)\}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-16 20:00:15
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