Stelsels combinatie

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Combinatie

1. \(\left\{\begin{matrix}-3x-3y=-24\\7y-9x=24\end{matrix}\right.\)
2. \(\left\{\begin{matrix}-8y=64+8x\\6x-9y=42\end{matrix}\right.\)
3. \(\left\{\begin{matrix}-5x+4y=11\\-9y-9x=117\end{matrix}\right.\)
4. \(\left\{\begin{matrix}-5y-9x=87\\3x+9y=-51\end{matrix}\right.\)
5. \(\left\{\begin{matrix}-3x+10y=-26\\7x-5y=24\end{matrix}\right.\)
6. \(\left\{\begin{matrix}-3x-6y=-12\\-2x=-10y+34\end{matrix}\right.\)
7. \(\left\{\begin{matrix}5y=-49+8x\\-10x-6y=0\end{matrix}\right.\)
8. \(\left\{\begin{matrix}9y=87-8x\\5x+3y=36\end{matrix}\right.\)
9. \(\left\{\begin{matrix}6x-2y=50\\-10x+10y=-50\end{matrix}\right.\)
10. \(\left\{\begin{matrix}5x-8y=-50\\9x+3y=84\end{matrix}\right.\)
11. \(\left\{\begin{matrix}-9x+10y=41\\-7x=-8y+33\end{matrix}\right.\)
12. \(\left\{\begin{matrix}4y+4x=16\\-7x-5y=-36\end{matrix}\right.\)

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Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}-3x-3y=-24\\7y-9x=24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x-3y=-24\\-9x+7y=24\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x-3y=-24& \color{red}{3.} & \color{blue}{7.} \\-9x+7y=24& \color{red}{-1.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-9x+9x}-9y-7y=-72-24} \\ \color{blue}{-21x-27x\underline{-21y+21y}=-168+72} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-16y=-96 \\-48x=-96\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-96}{-16}=6 \\x=\frac{-96}{-48}=2\end{matrix}\right.\\ \qquad V=\{(2,6)\}\)
2. \(\left\{\begin{matrix}-8y=64+8x\\6x-9y=42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-8y=64\\6x-9y=42\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-8y=64& \color{red}{3.} & \color{blue}{9.} \\6x-9y=42& \color{red}{4.} & \color{blue}{-8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}-24y-36y=192+168} \\ \color{blue}{-72x-48x\underline{-72y+72y}=576-336} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-60y=360 \\-120x=240\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{360}{-60}=-6 \\x=\frac{240}{-120}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-6)\}\)
3. \(\left\{\begin{matrix}-5x+4y=11\\-9y-9x=117\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+4y=11\\-9x-9y=117\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x+4y=11& \color{red}{9.} & \color{blue}{9.} \\-9x-9y=117& \color{red}{-5.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-45x+45x}+36y+45y=99-585} \\ \color{blue}{-45x-36x\underline{+36y-36y}=99+468} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}81y=-486 \\-81x=567\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-486}{81}=-6 \\x=\frac{567}{-81}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-6)\}\)
4. \(\left\{\begin{matrix}-5y-9x=87\\3x+9y=-51\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x-5y=87\\3x+9y=-51\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x-5y=87& \color{red}{1.} & \color{blue}{9.} \\3x+9y=-51& \color{red}{3.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-9x+9x}-5y+27y=87-153} \\ \color{blue}{-81x+15x\underline{-45y+45y}=783-255} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}22y=-66 \\-66x=528\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-66}{22}=-3 \\x=\frac{528}{-66}=-8\end{matrix}\right.\\ \qquad V=\{(-8,-3)\}\)
5. \(\left\{\begin{matrix}-3x+10y=-26\\7x-5y=24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+10y=-26& \color{red}{7.} & \color{blue}{1.} \\7x-5y=24& \color{red}{3.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-21x+21x}+70y-15y=-182+72} \\ \color{blue}{-3x+14x\underline{+10y-10y}=-26+48} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}55y=-110 \\11x=22\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-110}{55}=-2 \\x=\frac{22}{11}=2\end{matrix}\right.\\ \qquad V=\{(2,-2)\}\)
6. \(\left\{\begin{matrix}-3x-6y=-12\\-2x=-10y+34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x-6y=-12\\-2x+10y=34\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x-6y=-12& \color{red}{2.} & \color{blue}{5.} \\-2x+10y=34& \color{red}{-3.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}-12y-30y=-24-102} \\ \color{blue}{-15x-6x\underline{-30y+30y}=-60+102} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-42y=-126 \\-21x=42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-126}{-42}=3 \\x=\frac{42}{-21}=-2\end{matrix}\right.\\ \qquad V=\{(-2,3)\}\)
7. \(\left\{\begin{matrix}5y=-49+8x\\-10x-6y=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x+5y=-49\\-10x-6y=0\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x+5y=-49& \color{red}{5.} & \color{blue}{6.} \\-10x-6y=0& \color{red}{-4.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-40x+40x}+25y+24y=-245+0} \\ \color{blue}{-48x-50x\underline{+30y-30y}=-294+0} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}49y=-245 \\-98x=-294\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-245}{49}=-5 \\x=\frac{-294}{-98}=3\end{matrix}\right.\\ \qquad V=\{(3,-5)\}\)
8. \(\left\{\begin{matrix}9y=87-8x\\5x+3y=36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x+9y=87\\5x+3y=36\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+9y=87& \color{red}{5.} & \color{blue}{1.} \\5x+3y=36& \color{red}{-8.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{40x-40x}+45y-24y=435-288} \\ \color{blue}{8x-15x\underline{+9y-9y}=87-108} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}21y=147 \\-7x=-21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{147}{21}=7 \\x=\frac{-21}{-7}=3\end{matrix}\right.\\ \qquad V=\{(3,7)\}\)
9. \(\left\{\begin{matrix}6x-2y=50\\-10x+10y=-50\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-2y=50& \color{red}{5.} & \color{blue}{5.} \\-10x+10y=-50& \color{red}{3.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}-10y+30y=250-150} \\ \color{blue}{30x-10x\underline{-10y+10y}=250-50} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}20y=100 \\20x=200\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{100}{20}=5 \\x=\frac{200}{20}=10\end{matrix}\right.\\ \qquad V=\{(10,5)\}\)
10. \(\left\{\begin{matrix}5x-8y=-50\\9x+3y=84\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-8y=-50& \color{red}{9.} & \color{blue}{3.} \\9x+3y=84& \color{red}{-5.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{45x-45x}-72y-15y=-450-420} \\ \color{blue}{15x+72x\underline{-24y+24y}=-150+672} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-87y=-870 \\87x=522\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-870}{-87}=10 \\x=\frac{522}{87}=6\end{matrix}\right.\\ \qquad V=\{(6,10)\}\)
11. \(\left\{\begin{matrix}-9x+10y=41\\-7x=-8y+33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x+10y=41\\-7x+8y=33\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+10y=41& \color{red}{7.} & \color{blue}{4.} \\-7x+8y=33& \color{red}{-9.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-63x+63x}+70y-72y=287-297} \\ \color{blue}{-36x+35x\underline{+40y-40y}=164-165} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2y=-10 \\-x=-1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-10}{-2}=5 \\x=\frac{-1}{-1}=1\end{matrix}\right.\\ \qquad V=\{(1,5)\}\)
12. \(\left\{\begin{matrix}4y+4x=16\\-7x-5y=-36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+4y=16\\-7x-5y=-36\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+4y=16& \color{red}{7.} & \color{blue}{5.} \\-7x-5y=-36& \color{red}{4.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{28x-28x}+28y-20y=112-144} \\ \color{blue}{20x-28x\underline{+20y-20y}=80-144} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8y=-32 \\-8x=-64\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-32}{8}=-4 \\x=\frac{-64}{-8}=8\end{matrix}\right.\\ \qquad V=\{(8,-4)\}\)