Stelsels combinatie

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Combinatie

1. \(\left\{\begin{matrix}3y=66-6x\\3x-2y=19\end{matrix}\right.\)
2. \(\left\{\begin{matrix}-5x-4y=26\\10y-3x=-34\end{matrix}\right.\)
3. \(\left\{\begin{matrix}-5y+6x=88\\-8x+4y=-96\end{matrix}\right.\)
4. \(\left\{\begin{matrix}7x+8y=-108\\-5x=-7y-50\end{matrix}\right.\)
5. \(\left\{\begin{matrix}9x+3y=18\\8x=-4y+4\end{matrix}\right.\)
6. \(\left\{\begin{matrix}7x+3y=-31\\2x=5y+38\end{matrix}\right.\)
7. \(\left\{\begin{matrix}-4y=-86+6x\\6x-7y=-2\end{matrix}\right.\)
8. \(\left\{\begin{matrix}-2x+5y=0\\5x=-9y+43\end{matrix}\right.\)
9. \(\left\{\begin{matrix}3x-2y=-10\\-10x+5y=35\end{matrix}\right.\)
10. \(\left\{\begin{matrix}9x+4y=-1\\-3x+7y=17\end{matrix}\right.\)
11. \(\left\{\begin{matrix}2x-7y=-27\\10x-5y=-45\end{matrix}\right.\)
12. \(\left\{\begin{matrix}4y+10x=88\\-8x-6y=-62\end{matrix}\right.\)

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Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}3y=66-6x\\3x-2y=19\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+3y=66\\3x-2y=19\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x+3y=66& \color{red}{1.} & \color{blue}{2.} \\3x-2y=19& \color{red}{-2.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}+3y+4y=66-38} \\ \color{blue}{12x+9x\underline{+6y-6y}=132+57} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7y=28 \\21x=189\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{28}{7}=4 \\x=\frac{189}{21}=9\end{matrix}\right.\\ \qquad V=\{(9,4)\}\)
2. \(\left\{\begin{matrix}-5x-4y=26\\10y-3x=-34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-4y=26\\-3x+10y=-34\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-4y=26& \color{red}{3.} & \color{blue}{5.} \\-3x+10y=-34& \color{red}{-5.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-15x+15x}-12y-50y=78+170} \\ \color{blue}{-25x-6x\underline{-20y+20y}=130-68} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-62y=248 \\-31x=62\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{248}{-62}=-4 \\x=\frac{62}{-31}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-4)\}\)
3. \(\left\{\begin{matrix}-5y+6x=88\\-8x+4y=-96\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x-5y=88\\-8x+4y=-96\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-5y=88& \color{red}{4.} & \color{blue}{4.} \\-8x+4y=-96& \color{red}{3.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{24x-24x}-20y+12y=352-288} \\ \color{blue}{24x-40x\underline{-20y+20y}=352-480} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8y=64 \\-16x=-128\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{64}{-8}=-8 \\x=\frac{-128}{-16}=8\end{matrix}\right.\\ \qquad V=\{(8,-8)\}\)
4. \(\left\{\begin{matrix}7x+8y=-108\\-5x=-7y-50\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+8y=-108\\-5x+7y=-50\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+8y=-108& \color{red}{5.} & \color{blue}{7.} \\-5x+7y=-50& \color{red}{7.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{35x-35x}+40y+49y=-540-350} \\ \color{blue}{49x+40x\underline{+56y-56y}=-756+400} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}89y=-890 \\89x=-356\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-890}{89}=-10 \\x=\frac{-356}{89}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-10)\}\)
5. \(\left\{\begin{matrix}9x+3y=18\\8x=-4y+4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x+3y=18\\8x+4y=4\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+3y=18& \color{red}{8.} & \color{blue}{4.} \\8x+4y=4& \color{red}{-9.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{72x-72x}+24y-36y=144-36} \\ \color{blue}{36x-24x\underline{+12y-12y}=72-12} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-12y=108 \\12x=60\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{108}{-12}=-9 \\x=\frac{60}{12}=5\end{matrix}\right.\\ \qquad V=\{(5,-9)\}\)
6. \(\left\{\begin{matrix}7x+3y=-31\\2x=5y+38\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+3y=-31\\2x-5y=38\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+3y=-31& \color{red}{2.} & \color{blue}{5.} \\2x-5y=38& \color{red}{-7.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{14x-14x}+6y+35y=-62-266} \\ \color{blue}{35x+6x\underline{+15y-15y}=-155+114} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}41y=-328 \\41x=-41\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-328}{41}=-8 \\x=\frac{-41}{41}=-1\end{matrix}\right.\\ \qquad V=\{(-1,-8)\}\)
7. \(\left\{\begin{matrix}-4y=-86+6x\\6x-7y=-2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x-4y=-86\\6x-7y=-2\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-4y=-86& \color{red}{1.} & \color{blue}{7.} \\6x-7y=-2& \color{red}{1.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}-4y-7y=-86-2} \\ \color{blue}{-42x-24x\underline{-28y+28y}=-602+8} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-11y=-88 \\-66x=-594\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-88}{-11}=8 \\x=\frac{-594}{-66}=9\end{matrix}\right.\\ \qquad V=\{(9,8)\}\)
8. \(\left\{\begin{matrix}-2x+5y=0\\5x=-9y+43\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+5y=0\\5x+9y=43\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+5y=0& \color{red}{5.} & \color{blue}{9.} \\5x+9y=43& \color{red}{2.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}+25y+18y=0+86} \\ \color{blue}{-18x-25x\underline{+45y-45y}=0-215} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}43y=86 \\-43x=-215\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{86}{43}=2 \\x=\frac{-215}{-43}=5\end{matrix}\right.\\ \qquad V=\{(5,2)\}\)
9. \(\left\{\begin{matrix}3x-2y=-10\\-10x+5y=35\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-2y=-10& \color{red}{10.} & \color{blue}{5.} \\-10x+5y=35& \color{red}{3.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}-20y+15y=-100+105} \\ \color{blue}{15x-20x\underline{-10y+10y}=-50+70} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5y=5 \\-5x=20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{5}{-5}=-1 \\x=\frac{20}{-5}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-1)\}\)
10. \(\left\{\begin{matrix}9x+4y=-1\\-3x+7y=17\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+4y=-1& \color{red}{1.} & \color{blue}{7.} \\-3x+7y=17& \color{red}{3.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{9x-9x}+4y+21y=-1+51} \\ \color{blue}{63x+12x\underline{+28y-28y}=-7-68} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}25y=50 \\75x=-75\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{50}{25}=2 \\x=\frac{-75}{75}=-1\end{matrix}\right.\\ \qquad V=\{(-1,2)\}\)
11. \(\left\{\begin{matrix}2x-7y=-27\\10x-5y=-45\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x-7y=-27& \color{red}{5.} & \color{blue}{5.} \\10x-5y=-45& \color{red}{-1.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-35y+5y=-135+45} \\ \color{blue}{10x-70x\underline{-35y+35y}=-135+315} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-30y=-90 \\-60x=180\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-90}{-30}=3 \\x=\frac{180}{-60}=-3\end{matrix}\right.\\ \qquad V=\{(-3,3)\}\)
12. \(\left\{\begin{matrix}4y+10x=88\\-8x-6y=-62\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x+4y=88\\-8x-6y=-62\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x+4y=88& \color{red}{4.} & \color{blue}{3.} \\-8x-6y=-62& \color{red}{5.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}+16y-30y=352-310} \\ \color{blue}{30x-16x\underline{+12y-12y}=264-124} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-14y=42 \\14x=140\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{42}{-14}=-3 \\x=\frac{140}{14}=10\end{matrix}\right.\\ \qquad V=\{(10,-3)\}\)