Stelsels combinatie

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Combinatie

1. \(\left\{\begin{matrix}-2y=-48-6x\\9x+8y=-138\end{matrix}\right.\)
2. \(\left\{\begin{matrix}8x+6y=-98\\-2x=4y+32\end{matrix}\right.\)
3. \(\left\{\begin{matrix}-5x+4y=16\\-2y-8x=34\end{matrix}\right.\)
4. \(\left\{\begin{matrix}-10x+6y=14\\-3x=7y+13\end{matrix}\right.\)
5. \(\left\{\begin{matrix}-10y=20+4x\\-3x+9y=-84\end{matrix}\right.\)
6. \(\left\{\begin{matrix}-2x-6y=20\\3x=2y-8\end{matrix}\right.\)
7. \(\left\{\begin{matrix}2x+6y=-24\\-3y-4x=21\end{matrix}\right.\)
8. \(\left\{\begin{matrix}-9x+7y=29\\-10y+2x=2\end{matrix}\right.\)
9. \(\left\{\begin{matrix}10y-9x=-29\\-8x-8y=8\end{matrix}\right.\)
10. \(\left\{\begin{matrix}-7y=-11+3x\\7x-10y=-106\end{matrix}\right.\)
11. \(\left\{\begin{matrix}7x-3y=-29\\-10y+5x=50\end{matrix}\right.\)
12. \(\left\{\begin{matrix}-2x-3y=-32\\-7x-2y=-44\end{matrix}\right.\)

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Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}-2y=-48-6x\\9x+8y=-138\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x-2y=-48\\9x+8y=-138\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-2y=-48& \color{red}{3.} & \color{blue}{4.} \\9x+8y=-138& \color{red}{-2.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{18x-18x}-6y-16y=-144+276} \\ \color{blue}{24x+9x\underline{-8y+8y}=-192-138} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-22y=132 \\33x=-330\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{132}{-22}=-6 \\x=\frac{-330}{33}=-10\end{matrix}\right.\\ \qquad V=\{(-10,-6)\}\)
2. \(\left\{\begin{matrix}8x+6y=-98\\-2x=4y+32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x+6y=-98\\-2x-4y=32\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+6y=-98& \color{red}{1.} & \color{blue}{2.} \\-2x-4y=32& \color{red}{4.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}+6y-16y=-98+128} \\ \color{blue}{16x-6x\underline{+12y-12y}=-196+96} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10y=30 \\10x=-100\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{30}{-10}=-3 \\x=\frac{-100}{10}=-10\end{matrix}\right.\\ \qquad V=\{(-10,-3)\}\)
3. \(\left\{\begin{matrix}-5x+4y=16\\-2y-8x=34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+4y=16\\-8x-2y=34\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x+4y=16& \color{red}{8.} & \color{blue}{1.} \\-8x-2y=34& \color{red}{-5.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-40x+40x}+32y+10y=128-170} \\ \color{blue}{-5x-16x\underline{+4y-4y}=16+68} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}42y=-42 \\-21x=84\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-42}{42}=-1 \\x=\frac{84}{-21}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-1)\}\)
4. \(\left\{\begin{matrix}-10x+6y=14\\-3x=7y+13\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x+6y=14\\-3x-7y=13\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x+6y=14& \color{red}{3.} & \color{blue}{7.} \\-3x-7y=13& \color{red}{-10.} & \color{blue}{6.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}+18y+70y=42-130} \\ \color{blue}{-70x-18x\underline{+42y-42y}=98+78} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}88y=-88 \\-88x=176\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-88}{88}=-1 \\x=\frac{176}{-88}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-1)\}\)
5. \(\left\{\begin{matrix}-10y=20+4x\\-3x+9y=-84\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-10y=20\\-3x+9y=-84\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x-10y=20& \color{red}{3.} & \color{blue}{9.} \\-3x+9y=-84& \color{red}{-4.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-12x+12x}-30y-36y=60+336} \\ \color{blue}{-36x-30x\underline{-90y+90y}=180-840} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-66y=396 \\-66x=-660\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{396}{-66}=-6 \\x=\frac{-660}{-66}=10\end{matrix}\right.\\ \qquad V=\{(10,-6)\}\)
6. \(\left\{\begin{matrix}-2x-6y=20\\3x=2y-8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-6y=20\\3x-2y=-8\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x-6y=20& \color{red}{3.} & \color{blue}{1.} \\3x-2y=-8& \color{red}{2.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}-18y-4y=60-16} \\ \color{blue}{-2x-9x\underline{-6y+6y}=20+24} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-22y=44 \\-11x=44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{44}{-22}=-2 \\x=\frac{44}{-11}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-2)\}\)
7. \(\left\{\begin{matrix}2x+6y=-24\\-3y-4x=21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+6y=-24\\-4x-3y=21\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+6y=-24& \color{red}{2.} & \color{blue}{1.} \\-4x-3y=21& \color{red}{1.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{4x-4x}+12y-3y=-48+21} \\ \color{blue}{2x-8x\underline{+6y-6y}=-24+42} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9y=-27 \\-6x=18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-27}{9}=-3 \\x=\frac{18}{-6}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-3)\}\)
8. \(\left\{\begin{matrix}-9x+7y=29\\-10y+2x=2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x+7y=29\\2x-10y=2\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+7y=29& \color{red}{2.} & \color{blue}{10.} \\2x-10y=2& \color{red}{9.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}+14y-90y=58+18} \\ \color{blue}{-90x+14x\underline{+70y-70y}=290+14} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-76y=76 \\-76x=304\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{76}{-76}=-1 \\x=\frac{304}{-76}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-1)\}\)
9. \(\left\{\begin{matrix}10y-9x=-29\\-8x-8y=8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x+10y=-29\\-8x-8y=8\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+10y=-29& \color{red}{8.} & \color{blue}{4.} \\-8x-8y=8& \color{red}{-9.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-72x+72x}+80y+72y=-232-72} \\ \color{blue}{-36x-40x\underline{+40y-40y}=-116+40} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}152y=-304 \\-76x=-76\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-304}{152}=-2 \\x=\frac{-76}{-76}=1\end{matrix}\right.\\ \qquad V=\{(1,-2)\}\)
10. \(\left\{\begin{matrix}-7y=-11+3x\\7x-10y=-106\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x-7y=-11\\7x-10y=-106\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x-7y=-11& \color{red}{7.} & \color{blue}{10.} \\7x-10y=-106& \color{red}{3.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-21x+21x}-49y-30y=-77-318} \\ \color{blue}{-30x-49x\underline{-70y+70y}=-110+742} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-79y=-395 \\-79x=632\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-395}{-79}=5 \\x=\frac{632}{-79}=-8\end{matrix}\right.\\ \qquad V=\{(-8,5)\}\)
11. \(\left\{\begin{matrix}7x-3y=-29\\-10y+5x=50\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x-3y=-29\\5x-10y=50\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-3y=-29& \color{red}{5.} & \color{blue}{10.} \\5x-10y=50& \color{red}{-7.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{35x-35x}-15y+70y=-145-350} \\ \color{blue}{70x-15x\underline{-30y+30y}=-290-150} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}55y=-495 \\55x=-440\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-495}{55}=-9 \\x=\frac{-440}{55}=-8\end{matrix}\right.\\ \qquad V=\{(-8,-9)\}\)
12. \(\left\{\begin{matrix}-2x-3y=-32\\-7x-2y=-44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x-3y=-32& \color{red}{7.} & \color{blue}{2.} \\-7x-2y=-44& \color{red}{-2.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-14x+14x}-21y+4y=-224+88} \\ \color{blue}{-4x+21x\underline{-6y+6y}=-64+132} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-17y=-136 \\17x=68\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-136}{-17}=8 \\x=\frac{68}{17}=4\end{matrix}\right.\\ \qquad V=\{(4,8)\}\)