Stelsels combinatie

Hoofdmenu Eentje per keer 

Combinatie

  1. \(\left\{\begin{matrix}7x-7y=91\\2x+5y=5\end{matrix}\right.\)
  2. \(\left\{\begin{matrix}7y-5x=43\\3x-3y=-15\end{matrix}\right.\)
  3. \(\left\{\begin{matrix}-6y-9x=102\\7x+2y=-58\end{matrix}\right.\)
  4. \(\left\{\begin{matrix}6x-4y=-44\\-8x-7y=34\end{matrix}\right.\)
  5. \(\left\{\begin{matrix}5x+5y=5\\-8x-8y=-8\end{matrix}\right.\)
  6. \(\left\{\begin{matrix}-4x+3y=-1\\-8x=-8y-8\end{matrix}\right.\)
  7. \(\left\{\begin{matrix}-8y=-13-3x\\2x+2y=6\end{matrix}\right.\)
  8. \(\left\{\begin{matrix}-7x-5y=-6\\8y+7x=-3\end{matrix}\right.\)
  9. \(\left\{\begin{matrix}3x-6y=-57\\-4x=4y-44\end{matrix}\right.\)
  10. \(\left\{\begin{matrix}-3y=-65+7x\\-6x+9y=-21\end{matrix}\right.\)
  11. \(\left\{\begin{matrix}7y+8x=-38\\6x+4y=-16\end{matrix}\right.\)
  12. \(\left\{\begin{matrix}8x-10y=-20\\-8y-3x=-110\end{matrix}\right.\)

Combinatie

Verbetersleutel

  1. \(\left\{\begin{matrix}7x-7y=91\\2x+5y=5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-7y=91& \color{red}{2.} & \color{blue}{5.} \\2x+5y=5& \color{red}{-7.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{14x-14x}-14y-35y=182-35} \\ \color{blue}{35x+14x\underline{-35y+35y}=455+35} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-49y=147 \\49x=490\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{147}{-49}=-3 \\x=\frac{490}{49}=10\end{matrix}\right.\\ \qquad V=\{(10,-3)\}\)
  2. \(\left\{\begin{matrix}7y-5x=43\\3x-3y=-15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+7y=43\\3x-3y=-15\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x+7y=43& \color{red}{3.} & \color{blue}{3.} \\3x-3y=-15& \color{red}{5.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-15x+15x}+21y-15y=129-75} \\ \color{blue}{-15x+21x\underline{+21y-21y}=129-105} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6y=54 \\6x=24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{54}{6}=9 \\x=\frac{24}{6}=4\end{matrix}\right.\\ \qquad V=\{(4,9)\}\)
  3. \(\left\{\begin{matrix}-6y-9x=102\\7x+2y=-58\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x-6y=102\\7x+2y=-58\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x-6y=102& \color{red}{7.} & \color{blue}{1.} \\7x+2y=-58& \color{red}{9.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-63x+63x}-42y+18y=714-522} \\ \color{blue}{-9x+21x\underline{-6y+6y}=102-174} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-24y=192 \\12x=-72\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{192}{-24}=-8 \\x=\frac{-72}{12}=-6\end{matrix}\right.\\ \qquad V=\{(-6,-8)\}\)
  4. \(\left\{\begin{matrix}6x-4y=-44\\-8x-7y=34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-4y=-44& \color{red}{4.} & \color{blue}{7.} \\-8x-7y=34& \color{red}{3.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{24x-24x}-16y-21y=-176+102} \\ \color{blue}{42x+32x\underline{-28y+28y}=-308-136} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-37y=-74 \\74x=-444\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-74}{-37}=2 \\x=\frac{-444}{74}=-6\end{matrix}\right.\\ \qquad V=\{(-6,2)\}\)
  5. \(\left\{\begin{matrix}5x+5y=5\\-8x-8y=-8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x+5y=5& \color{red}{8.} & \color{blue}{8.} \\-8x-8y=-8& \color{red}{5.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}+40y-40y=40-40} \\ \color{blue}{40x-40x\underline{+40y-40y}=40-40} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}0y=0 \\0x=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{0}{0}=-3 \\x=\frac{0}{0}=4\end{matrix}\right.\\ \qquad V=\{(4,-3)\}\)
  6. \(\left\{\begin{matrix}-4x+3y=-1\\-8x=-8y-8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+3y=-1\\-8x+8y=-8\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x+3y=-1& \color{red}{2.} & \color{blue}{8.} \\-8x+8y=-8& \color{red}{-1.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-8x+8x}+6y-8y=-2+8} \\ \color{blue}{-32x+24x\underline{+24y-24y}=-8+24} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2y=6 \\-8x=16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{6}{-2}=-3 \\x=\frac{16}{-8}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-3)\}\)
  7. \(\left\{\begin{matrix}-8y=-13-3x\\2x+2y=6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-8y=-13\\2x+2y=6\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-8y=-13& \color{red}{2.} & \color{blue}{1.} \\2x+2y=6& \color{red}{-3.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}-16y-6y=-26-18} \\ \color{blue}{3x+8x\underline{-8y+8y}=-13+24} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-22y=-44 \\11x=11\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-44}{-22}=2 \\x=\frac{11}{11}=1\end{matrix}\right.\\ \qquad V=\{(1,2)\}\)
  8. \(\left\{\begin{matrix}-7x-5y=-6\\8y+7x=-3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-5y=-6\\7x+8y=-3\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-5y=-6& \color{red}{1.} & \color{blue}{8.} \\7x+8y=-3& \color{red}{1.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-7x+7x}-5y+8y=-6-3} \\ \color{blue}{-56x+35x\underline{-40y+40y}=-48-15} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3y=-9 \\-21x=-63\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-9}{3}=-3 \\x=\frac{-63}{-21}=3\end{matrix}\right.\\ \qquad V=\{(3,-3)\}\)
  9. \(\left\{\begin{matrix}3x-6y=-57\\-4x=4y-44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-6y=-57\\-4x-4y=-44\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-6y=-57& \color{red}{4.} & \color{blue}{2.} \\-4x-4y=-44& \color{red}{3.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{12x-12x}-24y-12y=-228-132} \\ \color{blue}{6x+12x\underline{-12y+12y}=-114+132} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-36y=-360 \\18x=18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-360}{-36}=10 \\x=\frac{18}{18}=1\end{matrix}\right.\\ \qquad V=\{(1,10)\}\)
  10. \(\left\{\begin{matrix}-3y=-65+7x\\-6x+9y=-21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-3y=-65\\-6x+9y=-21\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-3y=-65& \color{red}{6.} & \color{blue}{3.} \\-6x+9y=-21& \color{red}{-7.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-42x+42x}-18y-63y=-390+147} \\ \color{blue}{-21x-6x\underline{-9y+9y}=-195-21} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-81y=-243 \\-27x=-216\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-243}{-81}=3 \\x=\frac{-216}{-27}=8\end{matrix}\right.\\ \qquad V=\{(8,3)\}\)
  11. \(\left\{\begin{matrix}7y+8x=-38\\6x+4y=-16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x+7y=-38\\6x+4y=-16\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+7y=-38& \color{red}{3.} & \color{blue}{4.} \\6x+4y=-16& \color{red}{-4.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{24x-24x}+21y-16y=-114+64} \\ \color{blue}{32x-42x\underline{+28y-28y}=-152+112} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5y=-50 \\-10x=-40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-50}{5}=-10 \\x=\frac{-40}{-10}=4\end{matrix}\right.\\ \qquad V=\{(4,-10)\}\)
  12. \(\left\{\begin{matrix}8x-10y=-20\\-8y-3x=-110\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x-10y=-20\\-3x-8y=-110\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-10y=-20& \color{red}{3.} & \color{blue}{4.} \\-3x-8y=-110& \color{red}{8.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{24x-24x}-30y-64y=-60-880} \\ \color{blue}{32x+15x\underline{-40y+40y}=-80+550} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-94y=-940 \\47x=470\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-940}{-94}=10 \\x=\frac{470}{47}=10\end{matrix}\right.\\ \qquad V=\{(10,10)\}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-07 06:40:49
Een site van Busleyden Atheneum Mechelen