Stelsels combinatie

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Combinatie

1. \(\left\{\begin{matrix}-4y=-45+5x\\-3x+3y=27\end{matrix}\right.\)
2. \(\left\{\begin{matrix}7x-9y=74\\-2y+6x=52\end{matrix}\right.\)
3. \(\left\{\begin{matrix}-4x-10y=-34\\9y+3x=36\end{matrix}\right.\)
4. \(\left\{\begin{matrix}8x+7y=-16\\9x=-6y-33\end{matrix}\right.\)
5. \(\left\{\begin{matrix}9x-3y=87\\-7x+9y=-121\end{matrix}\right.\)
6. \(\left\{\begin{matrix}3x-3y=-9\\5x=5y-15\end{matrix}\right.\)
7. \(\left\{\begin{matrix}3x+4y=-24\\9y+2x=-35\end{matrix}\right.\)
8. \(\left\{\begin{matrix}-3y=1+5x\\-7x-6y=-4\end{matrix}\right.\)
9. \(\left\{\begin{matrix}5y=-2-8x\\-4x+10y=-24\end{matrix}\right.\)
10. \(\left\{\begin{matrix}2x+7y=3\\-4x=-10y+18\end{matrix}\right.\)
11. \(\left\{\begin{matrix}7x-5y=-78\\-3x-2y=21\end{matrix}\right.\)
12. \(\left\{\begin{matrix}4y-3x=-48\\-8x+3y=-59\end{matrix}\right.\)

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Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}-4y=-45+5x\\-3x+3y=27\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-4y=-45\\-3x+3y=27\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-4y=-45& \color{red}{3.} & \color{blue}{3.} \\-3x+3y=27& \color{red}{-5.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-15x+15x}-12y-15y=-135-135} \\ \color{blue}{-15x-12x\underline{-12y+12y}=-135+108} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-27y=-270 \\-27x=-27\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-270}{-27}=10 \\x=\frac{-27}{-27}=1\end{matrix}\right.\\ \qquad V=\{(1,10)\}\)
2. \(\left\{\begin{matrix}7x-9y=74\\-2y+6x=52\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x-9y=74\\6x-2y=52\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-9y=74& \color{red}{6.} & \color{blue}{2.} \\6x-2y=52& \color{red}{-7.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{42x-42x}-54y+14y=444-364} \\ \color{blue}{14x-54x\underline{-18y+18y}=148-468} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-40y=80 \\-40x=-320\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{80}{-40}=-2 \\x=\frac{-320}{-40}=8\end{matrix}\right.\\ \qquad V=\{(8,-2)\}\)
3. \(\left\{\begin{matrix}-4x-10y=-34\\9y+3x=36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-10y=-34\\3x+9y=36\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x-10y=-34& \color{red}{3.} & \color{blue}{9.} \\3x+9y=36& \color{red}{4.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-12x+12x}-30y+36y=-102+144} \\ \color{blue}{-36x+30x\underline{-90y+90y}=-306+360} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6y=42 \\-6x=54\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{42}{6}=7 \\x=\frac{54}{-6}=-9\end{matrix}\right.\\ \qquad V=\{(-9,7)\}\)
4. \(\left\{\begin{matrix}8x+7y=-16\\9x=-6y-33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x+7y=-16\\9x+6y=-33\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+7y=-16& \color{red}{9.} & \color{blue}{6.} \\9x+6y=-33& \color{red}{-8.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{72x-72x}+63y-48y=-144+264} \\ \color{blue}{48x-63x\underline{+42y-42y}=-96+231} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}15y=120 \\-15x=135\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{120}{15}=8 \\x=\frac{135}{-15}=-9\end{matrix}\right.\\ \qquad V=\{(-9,8)\}\)
5. \(\left\{\begin{matrix}9x-3y=87\\-7x+9y=-121\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x-3y=87& \color{red}{7.} & \color{blue}{3.} \\-7x+9y=-121& \color{red}{9.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{63x-63x}-21y+81y=609-1089} \\ \color{blue}{27x-7x\underline{-9y+9y}=261-121} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}60y=-480 \\20x=140\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-480}{60}=-8 \\x=\frac{140}{20}=7\end{matrix}\right.\\ \qquad V=\{(7,-8)\}\)
6. \(\left\{\begin{matrix}3x-3y=-9\\5x=5y-15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-3y=-9\\5x-5y=-15\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-3y=-9& \color{red}{5.} & \color{blue}{5.} \\5x-5y=-15& \color{red}{-3.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{15x-15x}-15y+15y=-45+45} \\ \color{blue}{15x-15x\underline{-15y+15y}=-45+45} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}0y=0 \\0x=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{0}{0}=-6 \\x=\frac{0}{0}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-6)\}\)
7. \(\left\{\begin{matrix}3x+4y=-24\\9y+2x=-35\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+4y=-24\\2x+9y=-35\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x+4y=-24& \color{red}{2.} & \color{blue}{9.} \\2x+9y=-35& \color{red}{-3.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}+8y-27y=-48+105} \\ \color{blue}{27x-8x\underline{+36y-36y}=-216+140} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-19y=57 \\19x=-76\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{57}{-19}=-3 \\x=\frac{-76}{19}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-3)\}\)
8. \(\left\{\begin{matrix}-3y=1+5x\\-7x-6y=-4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x-3y=1\\-7x-6y=-4\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x-3y=1& \color{red}{7.} & \color{blue}{2.} \\-7x-6y=-4& \color{red}{-5.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-35x+35x}-21y+30y=7+20} \\ \color{blue}{-10x+7x\underline{-6y+6y}=2+4} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9y=27 \\-3x=6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{27}{9}=3 \\x=\frac{6}{-3}=-2\end{matrix}\right.\\ \qquad V=\{(-2,3)\}\)
9. \(\left\{\begin{matrix}5y=-2-8x\\-4x+10y=-24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x+5y=-2\\-4x+10y=-24\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+5y=-2& \color{red}{1.} & \color{blue}{2.} \\-4x+10y=-24& \color{red}{2.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}+5y+20y=-2-48} \\ \color{blue}{16x+4x\underline{+10y-10y}=-4+24} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}25y=-50 \\20x=20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-50}{25}=-2 \\x=\frac{20}{20}=1\end{matrix}\right.\\ \qquad V=\{(1,-2)\}\)
10. \(\left\{\begin{matrix}2x+7y=3\\-4x=-10y+18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+7y=3\\-4x+10y=18\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+7y=3& \color{red}{2.} & \color{blue}{10.} \\-4x+10y=18& \color{red}{1.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{4x-4x}+14y+10y=6+18} \\ \color{blue}{20x+28x\underline{+70y-70y}=30-126} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}24y=24 \\48x=-96\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{24}{24}=1 \\x=\frac{-96}{48}=-2\end{matrix}\right.\\ \qquad V=\{(-2,1)\}\)
11. \(\left\{\begin{matrix}7x-5y=-78\\-3x-2y=21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-5y=-78& \color{red}{3.} & \color{blue}{2.} \\-3x-2y=21& \color{red}{7.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{21x-21x}-15y-14y=-234+147} \\ \color{blue}{14x+15x\underline{-10y+10y}=-156-105} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-29y=-87 \\29x=-261\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-87}{-29}=3 \\x=\frac{-261}{29}=-9\end{matrix}\right.\\ \qquad V=\{(-9,3)\}\)
12. \(\left\{\begin{matrix}4y-3x=-48\\-8x+3y=-59\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+4y=-48\\-8x+3y=-59\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+4y=-48& \color{red}{8.} & \color{blue}{3.} \\-8x+3y=-59& \color{red}{-3.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}+32y-9y=-384+177} \\ \color{blue}{-9x+32x\underline{+12y-12y}=-144+236} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}23y=-207 \\23x=92\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-207}{23}=-9 \\x=\frac{92}{23}=4\end{matrix}\right.\\ \qquad V=\{(4,-9)\}\)