Stelsels combinatie

Hoofdmenu Eentje per keer  🖨

Combinatie

1. \(\left\{\begin{matrix}8y-3x=11\\-6x-4y=62\end{matrix}\right.\)
2. \(\left\{\begin{matrix}-6x+8y=68\\10x=5y-55\end{matrix}\right.\)
3. \(\left\{\begin{matrix}4y=38-2x\\10x-2y=58\end{matrix}\right.\)
4. \(\left\{\begin{matrix}-8x+7y=96\\-7x=-10y+115\end{matrix}\right.\)
5. \(\left\{\begin{matrix}7y=6+9x\\-2x+10y=-24\end{matrix}\right.\)
6. \(\left\{\begin{matrix}-3x-10y=49\\6y-4x=-70\end{matrix}\right.\)
7. \(\left\{\begin{matrix}7y-6x=-17\\5x-2y=-5\end{matrix}\right.\)
8. \(\left\{\begin{matrix}10y=-98+8x\\-3x+2y=-28\end{matrix}\right.\)
9. \(\left\{\begin{matrix}-8y=72-8x\\10x-3y=41\end{matrix}\right.\)
10. \(\left\{\begin{matrix}9x-7y=83\\-2x=2y+10\end{matrix}\right.\)
11. \(\left\{\begin{matrix}8x+9y=67\\-4y+5x=13\end{matrix}\right.\)
12. \(\left\{\begin{matrix}-4y+7x=-16\\5x+5y=-90\end{matrix}\right.\)

---

Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}8y-3x=11\\-6x-4y=62\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+8y=11\\-6x-4y=62\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+8y=11& \color{red}{2.} & \color{blue}{1.} \\-6x-4y=62& \color{red}{-1.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+16y+4y=22-62} \\ \color{blue}{-3x-12x\underline{+8y-8y}=11+124} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}20y=-40 \\-15x=135\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-40}{20}=-2 \\x=\frac{135}{-15}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-2)\}\)
2. \(\left\{\begin{matrix}-6x+8y=68\\10x=5y-55\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+8y=68\\10x-5y=-55\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+8y=68& \color{red}{5.} & \color{blue}{5.} \\10x-5y=-55& \color{red}{3.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}+40y-15y=340-165} \\ \color{blue}{-30x+80x\underline{+40y-40y}=340-440} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}25y=175 \\50x=-100\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{175}{25}=7 \\x=\frac{-100}{50}=-2\end{matrix}\right.\\ \qquad V=\{(-2,7)\}\)
3. \(\left\{\begin{matrix}4y=38-2x\\10x-2y=58\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+4y=38\\10x-2y=58\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+4y=38& \color{red}{5.} & \color{blue}{1.} \\10x-2y=58& \color{red}{-1.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}+20y+2y=190-58} \\ \color{blue}{2x+20x\underline{+4y-4y}=38+116} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}22y=132 \\22x=154\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{132}{22}=6 \\x=\frac{154}{22}=7\end{matrix}\right.\\ \qquad V=\{(7,6)\}\)
4. \(\left\{\begin{matrix}-8x+7y=96\\-7x=-10y+115\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+7y=96\\-7x+10y=115\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+7y=96& \color{red}{7.} & \color{blue}{10.} \\-7x+10y=115& \color{red}{-8.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-56x+56x}+49y-80y=672-920} \\ \color{blue}{-80x+49x\underline{+70y-70y}=960-805} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-31y=-248 \\-31x=155\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-248}{-31}=8 \\x=\frac{155}{-31}=-5\end{matrix}\right.\\ \qquad V=\{(-5,8)\}\)
5. \(\left\{\begin{matrix}7y=6+9x\\-2x+10y=-24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x+7y=6\\-2x+10y=-24\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+7y=6& \color{red}{2.} & \color{blue}{10.} \\-2x+10y=-24& \color{red}{-9.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}+14y-90y=12+216} \\ \color{blue}{-90x+14x\underline{+70y-70y}=60+168} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-76y=228 \\-76x=228\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{228}{-76}=-3 \\x=\frac{228}{-76}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-3)\}\)
6. \(\left\{\begin{matrix}-3x-10y=49\\6y-4x=-70\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x-10y=49\\-4x+6y=-70\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x-10y=49& \color{red}{4.} & \color{blue}{3.} \\-4x+6y=-70& \color{red}{-3.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-12x+12x}-40y-18y=196+210} \\ \color{blue}{-9x-20x\underline{-30y+30y}=147-350} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-58y=406 \\-29x=-203\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{406}{-58}=-7 \\x=\frac{-203}{-29}=7\end{matrix}\right.\\ \qquad V=\{(7,-7)\}\)
7. \(\left\{\begin{matrix}7y-6x=-17\\5x-2y=-5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+7y=-17\\5x-2y=-5\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+7y=-17& \color{red}{5.} & \color{blue}{2.} \\5x-2y=-5& \color{red}{6.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}+35y-12y=-85-30} \\ \color{blue}{-12x+35x\underline{+14y-14y}=-34-35} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}23y=-115 \\23x=-69\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-115}{23}=-5 \\x=\frac{-69}{23}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-5)\}\)
8. \(\left\{\begin{matrix}10y=-98+8x\\-3x+2y=-28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+10y=-98\\-3x+2y=-28\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+10y=-98& \color{red}{3.} & \color{blue}{1.} \\-3x+2y=-28& \color{red}{-8.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}+30y-16y=-294+224} \\ \color{blue}{-8x+15x\underline{+10y-10y}=-98+140} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}14y=-70 \\7x=42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-70}{14}=-5 \\x=\frac{42}{7}=6\end{matrix}\right.\\ \qquad V=\{(6,-5)\}\)
9. \(\left\{\begin{matrix}-8y=72-8x\\10x-3y=41\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x-8y=72\\10x-3y=41\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-8y=72& \color{red}{5.} & \color{blue}{3.} \\10x-3y=41& \color{red}{-4.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}-40y+12y=360-164} \\ \color{blue}{24x-80x\underline{-24y+24y}=216-328} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-28y=196 \\-56x=-112\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{196}{-28}=-7 \\x=\frac{-112}{-56}=2\end{matrix}\right.\\ \qquad V=\{(2,-7)\}\)
10. \(\left\{\begin{matrix}9x-7y=83\\-2x=2y+10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x-7y=83\\-2x-2y=10\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x-7y=83& \color{red}{2.} & \color{blue}{2.} \\-2x-2y=10& \color{red}{9.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{18x-18x}-14y-18y=166+90} \\ \color{blue}{18x+14x\underline{-14y+14y}=166-70} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-32y=256 \\32x=96\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{256}{-32}=-8 \\x=\frac{96}{32}=3\end{matrix}\right.\\ \qquad V=\{(3,-8)\}\)
11. \(\left\{\begin{matrix}8x+9y=67\\-4y+5x=13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x+9y=67\\5x-4y=13\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+9y=67& \color{red}{5.} & \color{blue}{4.} \\5x-4y=13& \color{red}{-8.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}+45y+32y=335-104} \\ \color{blue}{32x+45x\underline{+36y-36y}=268+117} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}77y=231 \\77x=385\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{231}{77}=3 \\x=\frac{385}{77}=5\end{matrix}\right.\\ \qquad V=\{(5,3)\}\)
12. \(\left\{\begin{matrix}-4y+7x=-16\\5x+5y=-90\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x-4y=-16\\5x+5y=-90\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-4y=-16& \color{red}{5.} & \color{blue}{5.} \\5x+5y=-90& \color{red}{-7.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{35x-35x}-20y-35y=-80+630} \\ \color{blue}{35x+20x\underline{-20y+20y}=-80-360} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-55y=550 \\55x=-440\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{550}{-55}=-10 \\x=\frac{-440}{55}=-8\end{matrix}\right.\\ \qquad V=\{(-8,-10)\}\)