Stelsels combinatie

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Combinatie

1. \(\left\{\begin{matrix}2x-8y=-2\\3y-2x=-3\end{matrix}\right.\)
2. \(\left\{\begin{matrix}8x+3y=2\\-4x-8y=64\end{matrix}\right.\)
3. \(\left\{\begin{matrix}2x-10y=108\\-9x-7y=-18\end{matrix}\right.\)
4. \(\left\{\begin{matrix}-10y+7x=-25\\-5x+9y=29\end{matrix}\right.\)
5. \(\left\{\begin{matrix}-5y+10x=30\\-2x-10y=-72\end{matrix}\right.\)
6. \(\left\{\begin{matrix}4y=0-4x\\-5x-10y=5\end{matrix}\right.\)
7. \(\left\{\begin{matrix}10x+8y=-28\\5y+7x=-25\end{matrix}\right.\)
8. \(\left\{\begin{matrix}8x+10y=-36\\-5x=-8y-63\end{matrix}\right.\)
9. \(\left\{\begin{matrix}8x-3y=-59\\-6y+5x=-74\end{matrix}\right.\)
10. \(\left\{\begin{matrix}2y-3x=-9\\9x+5y=93\end{matrix}\right.\)
11. \(\left\{\begin{matrix}10x-7y=27\\-4x=3y-5\end{matrix}\right.\)
12. \(\left\{\begin{matrix}-2x+8y=-88\\3x=-3y-18\end{matrix}\right.\)

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Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}2x-8y=-2\\3y-2x=-3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x-8y=-2\\-2x+3y=-3\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x-8y=-2& \color{red}{1.} & \color{blue}{3.} \\-2x+3y=-3& \color{red}{1.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{2x-2x}-8y+3y=-2-3} \\ \color{blue}{6x-16x\underline{-24y+24y}=-6-24} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5y=-5 \\-10x=-30\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-5}{-5}=1 \\x=\frac{-30}{-10}=3\end{matrix}\right.\\ \qquad V=\{(3,1)\}\)
2. \(\left\{\begin{matrix}8x+3y=2\\-4x-8y=64\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+3y=2& \color{red}{1.} & \color{blue}{8.} \\-4x-8y=64& \color{red}{2.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}+3y-16y=2+128} \\ \color{blue}{64x-12x\underline{+24y-24y}=16+192} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-13y=130 \\52x=208\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{130}{-13}=-10 \\x=\frac{208}{52}=4\end{matrix}\right.\\ \qquad V=\{(4,-10)\}\)
3. \(\left\{\begin{matrix}2x-10y=108\\-9x-7y=-18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x-10y=108& \color{red}{9.} & \color{blue}{7.} \\-9x-7y=-18& \color{red}{2.} & \color{blue}{-10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{18x-18x}-90y-14y=972-36} \\ \color{blue}{14x+90x\underline{-70y+70y}=756+180} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-104y=936 \\104x=936\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{936}{-104}=-9 \\x=\frac{936}{104}=9\end{matrix}\right.\\ \qquad V=\{(9,-9)\}\)
4. \(\left\{\begin{matrix}-10y+7x=-25\\-5x+9y=29\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x-10y=-25\\-5x+9y=29\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-10y=-25& \color{red}{5.} & \color{blue}{9.} \\-5x+9y=29& \color{red}{7.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{35x-35x}-50y+63y=-125+203} \\ \color{blue}{63x-50x\underline{-90y+90y}=-225+290} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}13y=78 \\13x=65\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{78}{13}=6 \\x=\frac{65}{13}=5\end{matrix}\right.\\ \qquad V=\{(5,6)\}\)
5. \(\left\{\begin{matrix}-5y+10x=30\\-2x-10y=-72\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x-5y=30\\-2x-10y=-72\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-5y=30& \color{red}{1.} & \color{blue}{2.} \\-2x-10y=-72& \color{red}{5.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-5y-50y=30-360} \\ \color{blue}{20x+2x\underline{-10y+10y}=60+72} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-55y=-330 \\22x=132\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-330}{-55}=6 \\x=\frac{132}{22}=6\end{matrix}\right.\\ \qquad V=\{(6,6)\}\)
6. \(\left\{\begin{matrix}4y=0-4x\\-5x-10y=5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+4y=0\\-5x-10y=5\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+4y=0& \color{red}{5.} & \color{blue}{5.} \\-5x-10y=5& \color{red}{4.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}+20y-40y=0+20} \\ \color{blue}{20x-10x\underline{+20y-20y}=0+10} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-20y=20 \\10x=10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{20}{-20}=-1 \\x=\frac{10}{10}=1\end{matrix}\right.\\ \qquad V=\{(1,-1)\}\)
7. \(\left\{\begin{matrix}10x+8y=-28\\5y+7x=-25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x+8y=-28\\7x+5y=-25\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x+8y=-28& \color{red}{7.} & \color{blue}{5.} \\7x+5y=-25& \color{red}{-10.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{70x-70x}+56y-50y=-196+250} \\ \color{blue}{50x-56x\underline{+40y-40y}=-140+200} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6y=54 \\-6x=60\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{54}{6}=9 \\x=\frac{60}{-6}=-10\end{matrix}\right.\\ \qquad V=\{(-10,9)\}\)
8. \(\left\{\begin{matrix}8x+10y=-36\\-5x=-8y-63\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x+10y=-36\\-5x+8y=-63\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+10y=-36& \color{red}{5.} & \color{blue}{4.} \\-5x+8y=-63& \color{red}{8.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}+50y+64y=-180-504} \\ \color{blue}{32x+25x\underline{+40y-40y}=-144+315} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}114y=-684 \\57x=171\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-684}{114}=-6 \\x=\frac{171}{57}=3\end{matrix}\right.\\ \qquad V=\{(3,-6)\}\)
9. \(\left\{\begin{matrix}8x-3y=-59\\-6y+5x=-74\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x-3y=-59\\5x-6y=-74\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-3y=-59& \color{red}{5.} & \color{blue}{2.} \\5x-6y=-74& \color{red}{-8.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}-15y+48y=-295+592} \\ \color{blue}{16x-5x\underline{-6y+6y}=-118+74} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}33y=297 \\11x=-44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{297}{33}=9 \\x=\frac{-44}{11}=-4\end{matrix}\right.\\ \qquad V=\{(-4,9)\}\)
10. \(\left\{\begin{matrix}2y-3x=-9\\9x+5y=93\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+2y=-9\\9x+5y=93\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+2y=-9& \color{red}{3.} & \color{blue}{5.} \\9x+5y=93& \color{red}{1.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-9x+9x}+6y+5y=-27+93} \\ \color{blue}{-15x-18x\underline{+10y-10y}=-45-186} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}11y=66 \\-33x=-231\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{66}{11}=6 \\x=\frac{-231}{-33}=7\end{matrix}\right.\\ \qquad V=\{(7,6)\}\)
11. \(\left\{\begin{matrix}10x-7y=27\\-4x=3y-5\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x-7y=27\\-4x-3y=-5\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-7y=27& \color{red}{2.} & \color{blue}{3.} \\-4x-3y=-5& \color{red}{5.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}-14y-15y=54-25} \\ \color{blue}{30x+28x\underline{-21y+21y}=81+35} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-29y=29 \\58x=116\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{29}{-29}=-1 \\x=\frac{116}{58}=2\end{matrix}\right.\\ \qquad V=\{(2,-1)\}\)
12. \(\left\{\begin{matrix}-2x+8y=-88\\3x=-3y-18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+8y=-88\\3x+3y=-18\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+8y=-88& \color{red}{3.} & \color{blue}{3.} \\3x+3y=-18& \color{red}{2.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+24y+6y=-264-36} \\ \color{blue}{-6x-24x\underline{+24y-24y}=-264+144} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}30y=-300 \\-30x=-120\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-300}{30}=-10 \\x=\frac{-120}{-30}=4\end{matrix}\right.\\ \qquad V=\{(4,-10)\}\)