Stelsels combinatie

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Combinatie

1. \(\left\{\begin{matrix}-9x-6y=39\\2x=-4y-14\end{matrix}\right.\)
2. \(\left\{\begin{matrix}5x-4y=-7\\-8x=2y+28\end{matrix}\right.\)
3. \(\left\{\begin{matrix}-9y=109-10x\\-6x+5y=-65\end{matrix}\right.\)
4. \(\left\{\begin{matrix}-9y=-35-5x\\2x+7y=39\end{matrix}\right.\)
5. \(\left\{\begin{matrix}6x-4y=16\\-9x-7y=-11\end{matrix}\right.\)
6. \(\left\{\begin{matrix}-7x-6y=-9\\-5x=-3y-72\end{matrix}\right.\)
7. \(\left\{\begin{matrix}7x+10y=-99\\8x+6y=-86\end{matrix}\right.\)
8. \(\left\{\begin{matrix}6y-3x=-24\\-7x+2y=52\end{matrix}\right.\)
9. \(\left\{\begin{matrix}-7x+3y=19\\6x=-5y+14\end{matrix}\right.\)
10. \(\left\{\begin{matrix}3x+6y=39\\-6x-2y=-18\end{matrix}\right.\)
11. \(\left\{\begin{matrix}5x-8y=47\\-2x=-5y-35\end{matrix}\right.\)
12. \(\left\{\begin{matrix}-2y=30-8x\\-2x-8y=-84\end{matrix}\right.\)

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Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}-9x-6y=39\\2x=-4y-14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x-6y=39\\2x+4y=-14\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x-6y=39& \color{red}{2.} & \color{blue}{2.} \\2x+4y=-14& \color{red}{9.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}-12y+36y=78-126} \\ \color{blue}{-18x+6x\underline{-12y+12y}=78-42} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}24y=-48 \\-12x=36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-48}{24}=-2 \\x=\frac{36}{-12}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-2)\}\)
2. \(\left\{\begin{matrix}5x-4y=-7\\-8x=2y+28\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-4y=-7\\-8x-2y=28\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-4y=-7& \color{red}{8.} & \color{blue}{1.} \\-8x-2y=28& \color{red}{5.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}-32y-10y=-56+140} \\ \color{blue}{5x+16x\underline{-4y+4y}=-7-56} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-42y=84 \\21x=-63\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{84}{-42}=-2 \\x=\frac{-63}{21}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-2)\}\)
3. \(\left\{\begin{matrix}-9y=109-10x\\-6x+5y=-65\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x-9y=109\\-6x+5y=-65\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-9y=109& \color{red}{3.} & \color{blue}{5.} \\-6x+5y=-65& \color{red}{5.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}-27y+25y=327-325} \\ \color{blue}{50x-54x\underline{-45y+45y}=545-585} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2y=2 \\-4x=-40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{2}{-2}=-1 \\x=\frac{-40}{-4}=10\end{matrix}\right.\\ \qquad V=\{(10,-1)\}\)
4. \(\left\{\begin{matrix}-9y=-35-5x\\2x+7y=39\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-9y=-35\\2x+7y=39\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-9y=-35& \color{red}{2.} & \color{blue}{7.} \\2x+7y=39& \color{red}{-5.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-18y-35y=-70-195} \\ \color{blue}{35x+18x\underline{-63y+63y}=-245+351} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-53y=-265 \\53x=106\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-265}{-53}=5 \\x=\frac{106}{53}=2\end{matrix}\right.\\ \qquad V=\{(2,5)\}\)
5. \(\left\{\begin{matrix}6x-4y=16\\-9x-7y=-11\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-4y=16& \color{red}{3.} & \color{blue}{7.} \\-9x-7y=-11& \color{red}{2.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{18x-18x}-12y-14y=48-22} \\ \color{blue}{42x+36x\underline{-28y+28y}=112+44} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-26y=26 \\78x=156\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{26}{-26}=-1 \\x=\frac{156}{78}=2\end{matrix}\right.\\ \qquad V=\{(2,-1)\}\)
6. \(\left\{\begin{matrix}-7x-6y=-9\\-5x=-3y-72\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x-6y=-9\\-5x+3y=-72\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-6y=-9& \color{red}{5.} & \color{blue}{1.} \\-5x+3y=-72& \color{red}{-7.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-35x+35x}-30y-21y=-45+504} \\ \color{blue}{-7x-10x\underline{-6y+6y}=-9-144} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-51y=459 \\-17x=-153\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{459}{-51}=-9 \\x=\frac{-153}{-17}=9\end{matrix}\right.\\ \qquad V=\{(9,-9)\}\)
7. \(\left\{\begin{matrix}7x+10y=-99\\8x+6y=-86\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+10y=-99& \color{red}{8.} & \color{blue}{3.} \\8x+6y=-86& \color{red}{-7.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{56x-56x}+80y-42y=-792+602} \\ \color{blue}{21x-40x\underline{+30y-30y}=-297+430} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}38y=-190 \\-19x=133\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-190}{38}=-5 \\x=\frac{133}{-19}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-5)\}\)
8. \(\left\{\begin{matrix}6y-3x=-24\\-7x+2y=52\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+6y=-24\\-7x+2y=52\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+6y=-24& \color{red}{7.} & \color{blue}{1.} \\-7x+2y=52& \color{red}{-3.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-21x+21x}+42y-6y=-168-156} \\ \color{blue}{-3x+21x\underline{+6y-6y}=-24-156} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}36y=-324 \\18x=-180\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-324}{36}=-9 \\x=\frac{-180}{18}=-10\end{matrix}\right.\\ \qquad V=\{(-10,-9)\}\)
9. \(\left\{\begin{matrix}-7x+3y=19\\6x=-5y+14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x+3y=19\\6x+5y=14\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x+3y=19& \color{red}{6.} & \color{blue}{5.} \\6x+5y=14& \color{red}{7.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-42x+42x}+18y+35y=114+98} \\ \color{blue}{-35x-18x\underline{+15y-15y}=95-42} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}53y=212 \\-53x=53\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{212}{53}=4 \\x=\frac{53}{-53}=-1\end{matrix}\right.\\ \qquad V=\{(-1,4)\}\)
10. \(\left\{\begin{matrix}3x+6y=39\\-6x-2y=-18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+6y=39& \color{red}{2.} & \color{blue}{1.} \\-6x-2y=-18& \color{red}{1.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}+12y-2y=78-18} \\ \color{blue}{3x-18x\underline{+6y-6y}=39-54} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10y=60 \\-15x=-15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{60}{10}=6 \\x=\frac{-15}{-15}=1\end{matrix}\right.\\ \qquad V=\{(1,6)\}\)
11. \(\left\{\begin{matrix}5x-8y=47\\-2x=-5y-35\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-8y=47\\-2x+5y=-35\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-8y=47& \color{red}{2.} & \color{blue}{5.} \\-2x+5y=-35& \color{red}{5.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-16y+25y=94-175} \\ \color{blue}{25x-16x\underline{-40y+40y}=235-280} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9y=-81 \\9x=-45\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-81}{9}=-9 \\x=\frac{-45}{9}=-5\end{matrix}\right.\\ \qquad V=\{(-5,-9)\}\)
12. \(\left\{\begin{matrix}-2y=30-8x\\-2x-8y=-84\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x-2y=30\\-2x-8y=-84\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-2y=30& \color{red}{1.} & \color{blue}{4.} \\-2x-8y=-84& \color{red}{4.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}-2y-32y=30-336} \\ \color{blue}{32x+2x\underline{-8y+8y}=120+84} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-34y=-306 \\34x=204\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-306}{-34}=9 \\x=\frac{204}{34}=6\end{matrix}\right.\\ \qquad V=\{(6,9)\}\)