Stelsels combinatie

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Combinatie

1. \(\left\{\begin{matrix}8x+5y=49\\9x=-4y+60\end{matrix}\right.\)
2. \(\left\{\begin{matrix}-10x-5y=0\\10y+6x=-56\end{matrix}\right.\)
3. \(\left\{\begin{matrix}3x+10y=-68\\3y-6x=21\end{matrix}\right.\)
4. \(\left\{\begin{matrix}-2y=49-7x\\4x+5y=71\end{matrix}\right.\)
5. \(\left\{\begin{matrix}7x-5y=60\\7x+2y=25\end{matrix}\right.\)
6. \(\left\{\begin{matrix}-6x-7y=36\\-6x+6y=-42\end{matrix}\right.\)
7. \(\left\{\begin{matrix}5y-2x=-8\\-10x-3y=-96\end{matrix}\right.\)
8. \(\left\{\begin{matrix}10y=56-2x\\-9x+4y=42\end{matrix}\right.\)
9. \(\left\{\begin{matrix}5x-9y=-5\\-8y+5x=-10\end{matrix}\right.\)
10. \(\left\{\begin{matrix}-6x-10y=160\\3x+9y=-120\end{matrix}\right.\)
11. \(\left\{\begin{matrix}5y-3x=29\\6x-4y=-52\end{matrix}\right.\)
12. \(\left\{\begin{matrix}5y+6x=11\\8x-4y=-60\end{matrix}\right.\)

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Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}8x+5y=49\\9x=-4y+60\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x+5y=49\\9x+4y=60\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+5y=49& \color{red}{9.} & \color{blue}{4.} \\9x+4y=60& \color{red}{-8.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{72x-72x}+45y-32y=441-480} \\ \color{blue}{32x-45x\underline{+20y-20y}=196-300} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}13y=-39 \\-13x=-104\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-39}{13}=-3 \\x=\frac{-104}{-13}=8\end{matrix}\right.\\ \qquad V=\{(8,-3)\}\)
2. \(\left\{\begin{matrix}-10x-5y=0\\10y+6x=-56\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x-5y=0\\6x+10y=-56\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x-5y=0& \color{red}{3.} & \color{blue}{2.} \\6x+10y=-56& \color{red}{5.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}-15y+50y=0-280} \\ \color{blue}{-20x+6x\underline{-10y+10y}=0-56} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}35y=-280 \\-14x=-56\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-280}{35}=-8 \\x=\frac{-56}{-14}=4\end{matrix}\right.\\ \qquad V=\{(4,-8)\}\)
3. \(\left\{\begin{matrix}3x+10y=-68\\3y-6x=21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+10y=-68\\-6x+3y=21\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+10y=-68& \color{red}{2.} & \color{blue}{3.} \\-6x+3y=21& \color{red}{1.} & \color{blue}{-10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}+20y+3y=-136+21} \\ \color{blue}{9x+60x\underline{+30y-30y}=-204-210} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}23y=-115 \\69x=-414\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-115}{23}=-5 \\x=\frac{-414}{69}=-6\end{matrix}\right.\\ \qquad V=\{(-6,-5)\}\)
4. \(\left\{\begin{matrix}-2y=49-7x\\4x+5y=71\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x-2y=49\\4x+5y=71\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-2y=49& \color{red}{4.} & \color{blue}{5.} \\4x+5y=71& \color{red}{-7.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{28x-28x}-8y-35y=196-497} \\ \color{blue}{35x+8x\underline{-10y+10y}=245+142} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-43y=-301 \\43x=387\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-301}{-43}=7 \\x=\frac{387}{43}=9\end{matrix}\right.\\ \qquad V=\{(9,7)\}\)
5. \(\left\{\begin{matrix}7x-5y=60\\7x+2y=25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-5y=60& \color{red}{1.} & \color{blue}{2.} \\7x+2y=25& \color{red}{-1.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{7x-7x}-5y-2y=60-25} \\ \color{blue}{14x+35x\underline{-10y+10y}=120+125} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7y=35 \\49x=245\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{35}{-7}=-5 \\x=\frac{245}{49}=5\end{matrix}\right.\\ \qquad V=\{(5,-5)\}\)
6. \(\left\{\begin{matrix}-6x-7y=36\\-6x+6y=-42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-7y=36& \color{red}{1.} & \color{blue}{6.} \\-6x+6y=-42& \color{red}{-1.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}-7y-6y=36+42} \\ \color{blue}{-36x-42x\underline{-42y+42y}=216-294} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-13y=78 \\-78x=-78\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{78}{-13}=-6 \\x=\frac{-78}{-78}=1\end{matrix}\right.\\ \qquad V=\{(1,-6)\}\)
7. \(\left\{\begin{matrix}5y-2x=-8\\-10x-3y=-96\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+5y=-8\\-10x-3y=-96\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+5y=-8& \color{red}{5.} & \color{blue}{3.} \\-10x-3y=-96& \color{red}{-1.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}+25y+3y=-40+96} \\ \color{blue}{-6x-50x\underline{+15y-15y}=-24-480} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}28y=56 \\-56x=-504\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{56}{28}=2 \\x=\frac{-504}{-56}=9\end{matrix}\right.\\ \qquad V=\{(9,2)\}\)
8. \(\left\{\begin{matrix}10y=56-2x\\-9x+4y=42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+10y=56\\-9x+4y=42\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+10y=56& \color{red}{9.} & \color{blue}{2.} \\-9x+4y=42& \color{red}{2.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{18x-18x}+90y+8y=504+84} \\ \color{blue}{4x+45x\underline{+20y-20y}=112-210} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}98y=588 \\49x=-98\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{588}{98}=6 \\x=\frac{-98}{49}=-2\end{matrix}\right.\\ \qquad V=\{(-2,6)\}\)
9. \(\left\{\begin{matrix}5x-9y=-5\\-8y+5x=-10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-9y=-5\\5x-8y=-10\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-9y=-5& \color{red}{1.} & \color{blue}{8.} \\5x-8y=-10& \color{red}{-1.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{5x-5x}-9y+8y=-5+10} \\ \color{blue}{40x-45x\underline{-72y+72y}=-40+90} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-y=5 \\-5x=50\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{5}{-1}=-5 \\x=\frac{50}{-5}=-10\end{matrix}\right.\\ \qquad V=\{(-10,-5)\}\)
10. \(\left\{\begin{matrix}-6x-10y=160\\3x+9y=-120\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-10y=160& \color{red}{1.} & \color{blue}{9.} \\3x+9y=-120& \color{red}{2.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}-10y+18y=160-240} \\ \color{blue}{-54x+30x\underline{-90y+90y}=1440-1200} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8y=-80 \\-24x=240\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-80}{8}=-10 \\x=\frac{240}{-24}=-10\end{matrix}\right.\\ \qquad V=\{(-10,-10)\}\)
11. \(\left\{\begin{matrix}5y-3x=29\\6x-4y=-52\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+5y=29\\6x-4y=-52\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+5y=29& \color{red}{2.} & \color{blue}{4.} \\6x-4y=-52& \color{red}{1.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+10y-4y=58-52} \\ \color{blue}{-12x+30x\underline{+20y-20y}=116-260} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6y=6 \\18x=-144\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{6}{6}=1 \\x=\frac{-144}{18}=-8\end{matrix}\right.\\ \qquad V=\{(-8,1)\}\)
12. \(\left\{\begin{matrix}5y+6x=11\\8x-4y=-60\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+5y=11\\8x-4y=-60\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x+5y=11& \color{red}{4.} & \color{blue}{4.} \\8x-4y=-60& \color{red}{-3.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{24x-24x}+20y+12y=44+180} \\ \color{blue}{24x+40x\underline{+20y-20y}=44-300} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}32y=224 \\64x=-256\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{224}{32}=7 \\x=\frac{-256}{64}=-4\end{matrix}\right.\\ \qquad V=\{(-4,7)\}\)