Stelsels combinatie

Hoofdmenu Eentje per keer  🖨

Combinatie

1. \(\left\{\begin{matrix}6x-10y=-130\\-6y+10x=-110\end{matrix}\right.\)
2. \(\left\{\begin{matrix}-4y=4-4x\\-4x-8y=44\end{matrix}\right.\)
3. \(\left\{\begin{matrix}-6y-8x=-110\\5x-3y=35\end{matrix}\right.\)
4. \(\left\{\begin{matrix}-9y+5x=-11\\-9x+5y=-25\end{matrix}\right.\)
5. \(\left\{\begin{matrix}-10x+9y=18\\4x-10y=44\end{matrix}\right.\)
6. \(\left\{\begin{matrix}-6x-5y=-100\\5x=-8y+114\end{matrix}\right.\)
7. \(\left\{\begin{matrix}-7y=-39-10x\\-2x+9y=-15\end{matrix}\right.\)
8. \(\left\{\begin{matrix}6x-6y=-18\\6x=9y-30\end{matrix}\right.\)
9. \(\left\{\begin{matrix}2x-10y=-20\\8x=-4y+96\end{matrix}\right.\)
10. \(\left\{\begin{matrix}2y-7x=15\\6x-7y=-34\end{matrix}\right.\)
11. \(\left\{\begin{matrix}-6x+9y=-21\\6x+10y=-150\end{matrix}\right.\)
12. \(\left\{\begin{matrix}10y+7x=60\\-6x-8y=-52\end{matrix}\right.\)

---

Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}6x-10y=-130\\-6y+10x=-110\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x-10y=-130\\10x-6y=-110\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-10y=-130& \color{red}{5.} & \color{blue}{3.} \\10x-6y=-110& \color{red}{-3.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}-50y+18y=-650+330} \\ \color{blue}{18x-50x\underline{-30y+30y}=-390+550} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-32y=-320 \\-32x=160\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-320}{-32}=10 \\x=\frac{160}{-32}=-5\end{matrix}\right.\\ \qquad V=\{(-5,10)\}\)
2. \(\left\{\begin{matrix}-4y=4-4x\\-4x-8y=44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-4y=4\\-4x-8y=44\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x-4y=4& \color{red}{1.} & \color{blue}{2.} \\-4x-8y=44& \color{red}{1.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{4x-4x}-4y-8y=4+44} \\ \color{blue}{8x+4x\underline{-8y+8y}=8-44} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-12y=48 \\12x=-36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{48}{-12}=-4 \\x=\frac{-36}{12}=-3\end{matrix}\right.\\ \qquad V=\{(-3,-4)\}\)
3. \(\left\{\begin{matrix}-6y-8x=-110\\5x-3y=35\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-6y=-110\\5x-3y=35\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-6y=-110& \color{red}{5.} & \color{blue}{1.} \\5x-3y=35& \color{red}{8.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-40x+40x}-30y-24y=-550+280} \\ \color{blue}{-8x-10x\underline{-6y+6y}=-110-70} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-54y=-270 \\-18x=-180\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-270}{-54}=5 \\x=\frac{-180}{-18}=10\end{matrix}\right.\\ \qquad V=\{(10,5)\}\)
4. \(\left\{\begin{matrix}-9y+5x=-11\\-9x+5y=-25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-9y=-11\\-9x+5y=-25\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-9y=-11& \color{red}{9.} & \color{blue}{5.} \\-9x+5y=-25& \color{red}{5.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{45x-45x}-81y+25y=-99-125} \\ \color{blue}{25x-81x\underline{-45y+45y}=-55-225} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-56y=-224 \\-56x=-280\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-224}{-56}=4 \\x=\frac{-280}{-56}=5\end{matrix}\right.\\ \qquad V=\{(5,4)\}\)
5. \(\left\{\begin{matrix}-10x+9y=18\\4x-10y=44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x+9y=18& \color{red}{2.} & \color{blue}{10.} \\4x-10y=44& \color{red}{5.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-20x+20x}+18y-50y=36+220} \\ \color{blue}{-100x+36x\underline{+90y-90y}=180+396} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-32y=256 \\-64x=576\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{256}{-32}=-8 \\x=\frac{576}{-64}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-8)\}\)
6. \(\left\{\begin{matrix}-6x-5y=-100\\5x=-8y+114\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x-5y=-100\\5x+8y=114\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-5y=-100& \color{red}{5.} & \color{blue}{8.} \\5x+8y=114& \color{red}{6.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}-25y+48y=-500+684} \\ \color{blue}{-48x+25x\underline{-40y+40y}=-800+570} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}23y=184 \\-23x=-230\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{184}{23}=8 \\x=\frac{-230}{-23}=10\end{matrix}\right.\\ \qquad V=\{(10,8)\}\)
7. \(\left\{\begin{matrix}-7y=-39-10x\\-2x+9y=-15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x-7y=-39\\-2x+9y=-15\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x-7y=-39& \color{red}{1.} & \color{blue}{9.} \\-2x+9y=-15& \color{red}{5.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}-7y+45y=-39-75} \\ \color{blue}{90x-14x\underline{-63y+63y}=-351-105} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}38y=-114 \\76x=-456\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-114}{38}=-3 \\x=\frac{-456}{76}=-6\end{matrix}\right.\\ \qquad V=\{(-6,-3)\}\)
8. \(\left\{\begin{matrix}6x-6y=-18\\6x=9y-30\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x-6y=-18\\6x-9y=-30\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-6y=-18& \color{red}{1.} & \color{blue}{3.} \\6x-9y=-30& \color{red}{-1.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}-6y+9y=-18+30} \\ \color{blue}{18x-12x\underline{-18y+18y}=-54+60} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3y=12 \\6x=6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{12}{3}=4 \\x=\frac{6}{6}=1\end{matrix}\right.\\ \qquad V=\{(1,4)\}\)
9. \(\left\{\begin{matrix}2x-10y=-20\\8x=-4y+96\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x-10y=-20\\8x+4y=96\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x-10y=-20& \color{red}{4.} & \color{blue}{2.} \\8x+4y=96& \color{red}{-1.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}-40y-4y=-80-96} \\ \color{blue}{4x+40x\underline{-20y+20y}=-40+480} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-44y=-176 \\44x=440\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-176}{-44}=4 \\x=\frac{440}{44}=10\end{matrix}\right.\\ \qquad V=\{(10,4)\}\)
10. \(\left\{\begin{matrix}2y-7x=15\\6x-7y=-34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x+2y=15\\6x-7y=-34\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x+2y=15& \color{red}{6.} & \color{blue}{7.} \\6x-7y=-34& \color{red}{7.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-42x+42x}+12y-49y=90-238} \\ \color{blue}{-49x+12x\underline{+14y-14y}=105-68} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-37y=-148 \\-37x=37\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-148}{-37}=4 \\x=\frac{37}{-37}=-1\end{matrix}\right.\\ \qquad V=\{(-1,4)\}\)
11. \(\left\{\begin{matrix}-6x+9y=-21\\6x+10y=-150\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+9y=-21& \color{red}{1.} & \color{blue}{10.} \\6x+10y=-150& \color{red}{1.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+9y+10y=-21-150} \\ \color{blue}{-60x-54x\underline{+90y-90y}=-210+1350} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}19y=-171 \\-114x=1140\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-171}{19}=-9 \\x=\frac{1140}{-114}=-10\end{matrix}\right.\\ \qquad V=\{(-10,-9)\}\)
12. \(\left\{\begin{matrix}10y+7x=60\\-6x-8y=-52\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+10y=60\\-6x-8y=-52\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+10y=60& \color{red}{6.} & \color{blue}{4.} \\-6x-8y=-52& \color{red}{7.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{42x-42x}+60y-56y=360-364} \\ \color{blue}{28x-30x\underline{+40y-40y}=240-260} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4y=-4 \\-2x=-20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-4}{4}=-1 \\x=\frac{-20}{-2}=10\end{matrix}\right.\\ \qquad V=\{(10,-1)\}\)