Stelsels combinatie

Hoofdmenu Eentje per keer  🖨

Combinatie

1. \(\left\{\begin{matrix}-7x+6y=16\\-10y+4x=4\end{matrix}\right.\)
2. \(\left\{\begin{matrix}-10y+5x=-5\\3x+2y=-35\end{matrix}\right.\)
3. \(\left\{\begin{matrix}10x+4y=12\\-2y-5x=-6\end{matrix}\right.\)
4. \(\left\{\begin{matrix}8x-9y=47\\8x=8y+40\end{matrix}\right.\)
5. \(\left\{\begin{matrix}-8y=-37-3x\\4x-6y=-12\end{matrix}\right.\)
6. \(\left\{\begin{matrix}-9y=-12+8x\\-10x-10y=-20\end{matrix}\right.\)
7. \(\left\{\begin{matrix}2x-7y=32\\-3x=-9y-39\end{matrix}\right.\)
8. \(\left\{\begin{matrix}-3x+2y=-38\\-4y+5x=66\end{matrix}\right.\)
9. \(\left\{\begin{matrix}9y=-31+2x\\-3x+7y=-14\end{matrix}\right.\)
10. \(\left\{\begin{matrix}5x-7y=-24\\9x-6y=-63\end{matrix}\right.\)
11. \(\left\{\begin{matrix}2y+9x=-80\\9x-9y=-135\end{matrix}\right.\)
12. \(\left\{\begin{matrix}10y=63+9x\\6x+2y=36\end{matrix}\right.\)

---

Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}-7x+6y=16\\-10y+4x=4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x+6y=16\\4x-10y=4\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x+6y=16& \color{red}{4.} & \color{blue}{5.} \\4x-10y=4& \color{red}{7.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-28x+28x}+24y-70y=64+28} \\ \color{blue}{-35x+12x\underline{+30y-30y}=80+12} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-46y=92 \\-23x=92\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{92}{-46}=-2 \\x=\frac{92}{-23}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-2)\}\)
2. \(\left\{\begin{matrix}-10y+5x=-5\\3x+2y=-35\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-10y=-5\\3x+2y=-35\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-10y=-5& \color{red}{3.} & \color{blue}{1.} \\3x+2y=-35& \color{red}{-5.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{15x-15x}-30y-10y=-15+175} \\ \color{blue}{5x+15x\underline{-10y+10y}=-5-175} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-40y=160 \\20x=-180\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{160}{-40}=-4 \\x=\frac{-180}{20}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-4)\}\)
3. \(\left\{\begin{matrix}10x+4y=12\\-2y-5x=-6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}10x+4y=12\\-5x-2y=-6\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}10x+4y=12& \color{red}{1.} & \color{blue}{1.} \\-5x-2y=-6& \color{red}{2.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{10x-10x}+4y-4y=12-12} \\ \color{blue}{10x-10x\underline{+4y-4y}=12-12} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}0y=0 \\0x=0\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{0}{0}=-7 \\x=\frac{0}{0}=4\end{matrix}\right.\\ \qquad V=\{(4,-7)\}\)
4. \(\left\{\begin{matrix}8x-9y=47\\8x=8y+40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x-9y=47\\8x-8y=40\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-9y=47& \color{red}{1.} & \color{blue}{8.} \\8x-8y=40& \color{red}{-1.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}-9y+8y=47-40} \\ \color{blue}{64x-72x\underline{-72y+72y}=376-360} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-y=7 \\-8x=16\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{7}{-1}=-7 \\x=\frac{16}{-8}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-7)\}\)
5. \(\left\{\begin{matrix}-8y=-37-3x\\4x-6y=-12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-8y=-37\\4x-6y=-12\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-8y=-37& \color{red}{4.} & \color{blue}{3.} \\4x-6y=-12& \color{red}{-3.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{12x-12x}-32y+18y=-148+36} \\ \color{blue}{9x-16x\underline{-24y+24y}=-111+48} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-14y=-112 \\-7x=-63\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-112}{-14}=8 \\x=\frac{-63}{-7}=9\end{matrix}\right.\\ \qquad V=\{(9,8)\}\)
6. \(\left\{\begin{matrix}-9y=-12+8x\\-10x-10y=-20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-8x-9y=-12\\-10x-10y=-20\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-8x-9y=-12& \color{red}{5.} & \color{blue}{10.} \\-10x-10y=-20& \color{red}{-4.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-40x+40x}-45y+40y=-60+80} \\ \color{blue}{-80x+90x\underline{-90y+90y}=-120+180} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5y=20 \\10x=60\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{20}{-5}=-4 \\x=\frac{60}{10}=6\end{matrix}\right.\\ \qquad V=\{(6,-4)\}\)
7. \(\left\{\begin{matrix}2x-7y=32\\-3x=-9y-39\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x-7y=32\\-3x+9y=-39\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x-7y=32& \color{red}{3.} & \color{blue}{9.} \\-3x+9y=-39& \color{red}{2.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}-21y+18y=96-78} \\ \color{blue}{18x-21x\underline{-63y+63y}=288-273} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3y=18 \\-3x=15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{18}{-3}=-6 \\x=\frac{15}{-3}=-5\end{matrix}\right.\\ \qquad V=\{(-5,-6)\}\)
8. \(\left\{\begin{matrix}-3x+2y=-38\\-4y+5x=66\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+2y=-38\\5x-4y=66\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+2y=-38& \color{red}{5.} & \color{blue}{2.} \\5x-4y=66& \color{red}{3.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-15x+15x}+10y-12y=-190+198} \\ \color{blue}{-6x+5x\underline{+4y-4y}=-76+66} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2y=8 \\-x=-10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{8}{-2}=-4 \\x=\frac{-10}{-1}=10\end{matrix}\right.\\ \qquad V=\{(10,-4)\}\)
9. \(\left\{\begin{matrix}9y=-31+2x\\-3x+7y=-14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x+9y=-31\\-3x+7y=-14\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+9y=-31& \color{red}{3.} & \color{blue}{7.} \\-3x+7y=-14& \color{red}{-2.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+27y-14y=-93+28} \\ \color{blue}{-14x+27x\underline{+63y-63y}=-217+126} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}13y=-65 \\13x=-91\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-65}{13}=-5 \\x=\frac{-91}{13}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-5)\}\)
10. \(\left\{\begin{matrix}5x-7y=-24\\9x-6y=-63\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-7y=-24& \color{red}{9.} & \color{blue}{6.} \\9x-6y=-63& \color{red}{-5.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{45x-45x}-63y+30y=-216+315} \\ \color{blue}{30x-63x\underline{-42y+42y}=-144+441} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-33y=99 \\-33x=297\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{99}{-33}=-3 \\x=\frac{297}{-33}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-3)\}\)
11. \(\left\{\begin{matrix}2y+9x=-80\\9x-9y=-135\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9x+2y=-80\\9x-9y=-135\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+2y=-80& \color{red}{1.} & \color{blue}{9.} \\9x-9y=-135& \color{red}{-1.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{9x-9x}+2y+9y=-80+135} \\ \color{blue}{81x+18x\underline{+18y-18y}=-720-270} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}11y=55 \\99x=-990\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{55}{11}=5 \\x=\frac{-990}{99}=-10\end{matrix}\right.\\ \qquad V=\{(-10,5)\}\)
12. \(\left\{\begin{matrix}10y=63+9x\\6x+2y=36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x+10y=63\\6x+2y=36\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+10y=63& \color{red}{2.} & \color{blue}{1.} \\6x+2y=36& \color{red}{3.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}+20y+6y=126+108} \\ \color{blue}{-9x-30x\underline{+10y-10y}=63-180} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}26y=234 \\-39x=-117\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{234}{26}=9 \\x=\frac{-117}{-39}=3\end{matrix}\right.\\ \qquad V=\{(3,9)\}\)