Stelsels combinatie

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Combinatie

1. \(\left\{\begin{matrix}2y=20+2x\\-6x-3y=-3\end{matrix}\right.\)
2. \(\left\{\begin{matrix}-9y+5x=40\\5x+8y=-45\end{matrix}\right.\)
3. \(\left\{\begin{matrix}-8y=-48+6x\\-2x+2y=-2\end{matrix}\right.\)
4. \(\left\{\begin{matrix}-8x-10y=-54\\-5y-3x=-29\end{matrix}\right.\)
5. \(\left\{\begin{matrix}-4y=8+2x\\-4x-9y=22\end{matrix}\right.\)
6. \(\left\{\begin{matrix}10y=-52+4x\\10x-4y=88\end{matrix}\right.\)
7. \(\left\{\begin{matrix}6y=48-10x\\3x+7y=4\end{matrix}\right.\)
8. \(\left\{\begin{matrix}2y=-50+4x\\9x+8y=0\end{matrix}\right.\)
9. \(\left\{\begin{matrix}-5y=-36-3x\\-7x-6y=31\end{matrix}\right.\)
10. \(\left\{\begin{matrix}2y=28+9x\\4x-8y=-48\end{matrix}\right.\)
11. \(\left\{\begin{matrix}9x+10y=61\\2x-2y=-16\end{matrix}\right.\)
12. \(\left\{\begin{matrix}-9x+6y=-21\\-8x=9y-33\end{matrix}\right.\)

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Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}2y=20+2x\\-6x-3y=-3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+2y=20\\-6x-3y=-3\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+2y=20& \color{red}{3.} & \color{blue}{3.} \\-6x-3y=-3& \color{red}{-1.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+6y+3y=60+3} \\ \color{blue}{-6x-12x\underline{+6y-6y}=60-6} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9y=63 \\-18x=54\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{63}{9}=7 \\x=\frac{54}{-18}=-3\end{matrix}\right.\\ \qquad V=\{(-3,7)\}\)
2. \(\left\{\begin{matrix}-9y+5x=40\\5x+8y=-45\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-9y=40\\5x+8y=-45\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-9y=40& \color{red}{1.} & \color{blue}{8.} \\5x+8y=-45& \color{red}{-1.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{5x-5x}-9y-8y=40+45} \\ \color{blue}{40x+45x\underline{-72y+72y}=320-405} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-17y=85 \\85x=-85\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{85}{-17}=-5 \\x=\frac{-85}{85}=-1\end{matrix}\right.\\ \qquad V=\{(-1,-5)\}\)
3. \(\left\{\begin{matrix}-8y=-48+6x\\-2x+2y=-2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x-8y=-48\\-2x+2y=-2\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-8y=-48& \color{red}{1.} & \color{blue}{1.} \\-2x+2y=-2& \color{red}{-3.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}-8y-6y=-48+6} \\ \color{blue}{-6x-8x\underline{-8y+8y}=-48-8} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-14y=-42 \\-14x=-56\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-42}{-14}=3 \\x=\frac{-56}{-14}=4\end{matrix}\right.\\ \qquad V=\{(4,3)\}\)
4. \(\left\{\begin{matrix}-8x-10y=-54\\-5y-3x=-29\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-10y=-54\\-3x-5y=-29\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-10y=-54& \color{red}{3.} & \color{blue}{1.} \\-3x-5y=-29& \color{red}{-8.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}-30y+40y=-162+232} \\ \color{blue}{-8x+6x\underline{-10y+10y}=-54+58} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10y=70 \\-2x=4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{70}{10}=7 \\x=\frac{4}{-2}=-2\end{matrix}\right.\\ \qquad V=\{(-2,7)\}\)
5. \(\left\{\begin{matrix}-4y=8+2x\\-4x-9y=22\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-4y=8\\-4x-9y=22\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x-4y=8& \color{red}{2.} & \color{blue}{9.} \\-4x-9y=22& \color{red}{-1.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-4x+4x}-8y+9y=16-22} \\ \color{blue}{-18x+16x\underline{-36y+36y}=72-88} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-6 \\-2x=-16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-6}{1}=-6 \\x=\frac{-16}{-2}=8\end{matrix}\right.\\ \qquad V=\{(8,-6)\}\)
6. \(\left\{\begin{matrix}10y=-52+4x\\10x-4y=88\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+10y=-52\\10x-4y=88\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x+10y=-52& \color{red}{5.} & \color{blue}{2.} \\10x-4y=88& \color{red}{2.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-20x+20x}+50y-8y=-260+176} \\ \color{blue}{-8x+50x\underline{+20y-20y}=-104+440} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}42y=-84 \\42x=336\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-84}{42}=-2 \\x=\frac{336}{42}=8\end{matrix}\right.\\ \qquad V=\{(8,-2)\}\)
7. \(\left\{\begin{matrix}6y=48-10x\\3x+7y=4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x+6y=48\\3x+7y=4\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x+6y=48& \color{red}{3.} & \color{blue}{7.} \\3x+7y=4& \color{red}{-10.} & \color{blue}{-6.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}+18y-70y=144-40} \\ \color{blue}{70x-18x\underline{+42y-42y}=336-24} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-52y=104 \\52x=312\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{104}{-52}=-2 \\x=\frac{312}{52}=6\end{matrix}\right.\\ \qquad V=\{(6,-2)\}\)
8. \(\left\{\begin{matrix}2y=-50+4x\\9x+8y=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+2y=-50\\9x+8y=0\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x+2y=-50& \color{red}{9.} & \color{blue}{4.} \\9x+8y=0& \color{red}{4.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-36x+36x}+18y+32y=-450+0} \\ \color{blue}{-16x-9x\underline{+8y-8y}=-200+0} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}50y=-450 \\-25x=-200\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-450}{50}=-9 \\x=\frac{-200}{-25}=8\end{matrix}\right.\\ \qquad V=\{(8,-9)\}\)
9. \(\left\{\begin{matrix}-5y=-36-3x\\-7x-6y=31\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-5y=-36\\-7x-6y=31\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-5y=-36& \color{red}{7.} & \color{blue}{6.} \\-7x-6y=31& \color{red}{3.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{21x-21x}-35y-18y=-252+93} \\ \color{blue}{18x+35x\underline{-30y+30y}=-216-155} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-53y=-159 \\53x=-371\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-159}{-53}=3 \\x=\frac{-371}{53}=-7\end{matrix}\right.\\ \qquad V=\{(-7,3)\}\)
10. \(\left\{\begin{matrix}2y=28+9x\\4x-8y=-48\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x+2y=28\\4x-8y=-48\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+2y=28& \color{red}{4.} & \color{blue}{4.} \\4x-8y=-48& \color{red}{9.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-36x+36x}+8y-72y=112-432} \\ \color{blue}{-36x+4x\underline{+8y-8y}=112-48} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-64y=-320 \\-32x=64\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-320}{-64}=5 \\x=\frac{64}{-32}=-2\end{matrix}\right.\\ \qquad V=\{(-2,5)\}\)
11. \(\left\{\begin{matrix}9x+10y=61\\2x-2y=-16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+10y=61& \color{red}{2.} & \color{blue}{1.} \\2x-2y=-16& \color{red}{-9.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{18x-18x}+20y+18y=122+144} \\ \color{blue}{9x+10x\underline{+10y-10y}=61-80} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}38y=266 \\19x=-19\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{266}{38}=7 \\x=\frac{-19}{19}=-1\end{matrix}\right.\\ \qquad V=\{(-1,7)\}\)
12. \(\left\{\begin{matrix}-9x+6y=-21\\-8x=9y-33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x+6y=-21\\-8x-9y=-33\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+6y=-21& \color{red}{8.} & \color{blue}{3.} \\-8x-9y=-33& \color{red}{-9.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-72x+72x}+48y+81y=-168+297} \\ \color{blue}{-27x-16x\underline{+18y-18y}=-63-66} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}129y=129 \\-43x=-129\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{129}{129}=1 \\x=\frac{-129}{-43}=3\end{matrix}\right.\\ \qquad V=\{(3,1)\}\)