Stelsels combinatie

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Combinatie

1. \(\left\{\begin{matrix}-8x-5y=-69\\8y-9x=-64\end{matrix}\right.\)
2. \(\left\{\begin{matrix}-9x+8y=-105\\4x+5y=21\end{matrix}\right.\)
3. \(\left\{\begin{matrix}5x-9y=56\\2y-2x=-16\end{matrix}\right.\)
4. \(\left\{\begin{matrix}10x+10y=-30\\4x=-5y-11\end{matrix}\right.\)
5. \(\left\{\begin{matrix}-5x-6y=-38\\-5x-8y=-54\end{matrix}\right.\)
6. \(\left\{\begin{matrix}-3y=-108-9x\\-4x+6y=90\end{matrix}\right.\)
7. \(\left\{\begin{matrix}-8y-9x=117\\10x-10y=40\end{matrix}\right.\)
8. \(\left\{\begin{matrix}-3x-9y=-36\\8x-6y=6\end{matrix}\right.\)
9. \(\left\{\begin{matrix}3x+4y=7\\2y-4x=42\end{matrix}\right.\)
10. \(\left\{\begin{matrix}8y-6x=-100\\7x-5y=82\end{matrix}\right.\)
11. \(\left\{\begin{matrix}6y-10x=4\\-5x+2y=-7\end{matrix}\right.\)
12. \(\left\{\begin{matrix}-7y+4x=-41\\-3x+3y=15\end{matrix}\right.\)

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Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}-8x-5y=-69\\8y-9x=-64\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-5y=-69\\-9x+8y=-64\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-5y=-69& \color{red}{9.} & \color{blue}{8.} \\-9x+8y=-64& \color{red}{-8.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-72x+72x}-45y-64y=-621+512} \\ \color{blue}{-64x-45x\underline{-40y+40y}=-552-320} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-109y=-109 \\-109x=-872\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-109}{-109}=1 \\x=\frac{-872}{-109}=8\end{matrix}\right.\\ \qquad V=\{(8,1)\}\)
2. \(\left\{\begin{matrix}-9x+8y=-105\\4x+5y=21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+8y=-105& \color{red}{4.} & \color{blue}{5.} \\4x+5y=21& \color{red}{9.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-36x+36x}+32y+45y=-420+189} \\ \color{blue}{-45x-32x\underline{+40y-40y}=-525-168} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}77y=-231 \\-77x=-693\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-231}{77}=-3 \\x=\frac{-693}{-77}=9\end{matrix}\right.\\ \qquad V=\{(9,-3)\}\)
3. \(\left\{\begin{matrix}5x-9y=56\\2y-2x=-16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-9y=56\\-2x+2y=-16\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-9y=56& \color{red}{2.} & \color{blue}{2.} \\-2x+2y=-16& \color{red}{5.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-18y+10y=112-80} \\ \color{blue}{10x-18x\underline{-18y+18y}=112-144} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8y=32 \\-8x=-32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{32}{-8}=-4 \\x=\frac{-32}{-8}=4\end{matrix}\right.\\ \qquad V=\{(4,-4)\}\)
4. \(\left\{\begin{matrix}10x+10y=-30\\4x=-5y-11\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x+10y=-30\\4x+5y=-11\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x+10y=-30& \color{red}{2.} & \color{blue}{1.} \\4x+5y=-11& \color{red}{-5.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}+20y-25y=-60+55} \\ \color{blue}{10x-8x\underline{+10y-10y}=-30+22} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5y=-5 \\2x=-8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-5}{-5}=1 \\x=\frac{-8}{2}=-4\end{matrix}\right.\\ \qquad V=\{(-4,1)\}\)
5. \(\left\{\begin{matrix}-5x-6y=-38\\-5x-8y=-54\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-6y=-38& \color{red}{1.} & \color{blue}{4.} \\-5x-8y=-54& \color{red}{-1.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-5x+5x}-6y+8y=-38+54} \\ \color{blue}{-20x+15x\underline{-24y+24y}=-152+162} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2y=16 \\-5x=10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{16}{2}=8 \\x=\frac{10}{-5}=-2\end{matrix}\right.\\ \qquad V=\{(-2,8)\}\)
6. \(\left\{\begin{matrix}-3y=-108-9x\\-4x+6y=90\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x-3y=-108\\-4x+6y=90\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x-3y=-108& \color{red}{4.} & \color{blue}{2.} \\-4x+6y=90& \color{red}{9.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{36x-36x}-12y+54y=-432+810} \\ \color{blue}{18x-4x\underline{-6y+6y}=-216+90} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}42y=378 \\14x=-126\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{378}{42}=9 \\x=\frac{-126}{14}=-9\end{matrix}\right.\\ \qquad V=\{(-9,9)\}\)
7. \(\left\{\begin{matrix}-8y-9x=117\\10x-10y=40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x-8y=117\\10x-10y=40\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x-8y=117& \color{red}{10.} & \color{blue}{5.} \\10x-10y=40& \color{red}{9.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-90x+90x}-80y-90y=1170+360} \\ \color{blue}{-45x-40x\underline{-40y+40y}=585-160} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-170y=1530 \\-85x=425\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{1530}{-170}=-9 \\x=\frac{425}{-85}=-5\end{matrix}\right.\\ \qquad V=\{(-5,-9)\}\)
8. \(\left\{\begin{matrix}-3x-9y=-36\\8x-6y=6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x-9y=-36& \color{red}{8.} & \color{blue}{2.} \\8x-6y=6& \color{red}{3.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}-72y-18y=-288+18} \\ \color{blue}{-6x-24x\underline{-18y+18y}=-72-18} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-90y=-270 \\-30x=-90\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-270}{-90}=3 \\x=\frac{-90}{-30}=3\end{matrix}\right.\\ \qquad V=\{(3,3)\}\)
9. \(\left\{\begin{matrix}3x+4y=7\\2y-4x=42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+4y=7\\-4x+2y=42\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+4y=7& \color{red}{4.} & \color{blue}{1.} \\-4x+2y=42& \color{red}{3.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{12x-12x}+16y+6y=28+126} \\ \color{blue}{3x+8x\underline{+4y-4y}=7-84} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}22y=154 \\11x=-77\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{154}{22}=7 \\x=\frac{-77}{11}=-7\end{matrix}\right.\\ \qquad V=\{(-7,7)\}\)
10. \(\left\{\begin{matrix}8y-6x=-100\\7x-5y=82\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+8y=-100\\7x-5y=82\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+8y=-100& \color{red}{7.} & \color{blue}{5.} \\7x-5y=82& \color{red}{6.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-42x+42x}+56y-30y=-700+492} \\ \color{blue}{-30x+56x\underline{+40y-40y}=-500+656} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}26y=-208 \\26x=156\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-208}{26}=-8 \\x=\frac{156}{26}=6\end{matrix}\right.\\ \qquad V=\{(6,-8)\}\)
11. \(\left\{\begin{matrix}6y-10x=4\\-5x+2y=-7\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x+6y=4\\-5x+2y=-7\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x+6y=4& \color{red}{1.} & \color{blue}{1.} \\-5x+2y=-7& \color{red}{-2.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}+6y-4y=4+14} \\ \color{blue}{-10x+15x\underline{+6y-6y}=4+21} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2y=18 \\5x=25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{18}{2}=9 \\x=\frac{25}{5}=5\end{matrix}\right.\\ \qquad V=\{(5,9)\}\)
12. \(\left\{\begin{matrix}-7y+4x=-41\\-3x+3y=15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-7y=-41\\-3x+3y=15\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x-7y=-41& \color{red}{3.} & \color{blue}{3.} \\-3x+3y=15& \color{red}{4.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{12x-12x}-21y+12y=-123+60} \\ \color{blue}{12x-21x\underline{-21y+21y}=-123+105} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9y=-63 \\-9x=-18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-63}{-9}=7 \\x=\frac{-18}{-9}=2\end{matrix}\right.\\ \qquad V=\{(2,7)\}\)