Stelsels combinatie

Hoofdmenu Eentje per keer  🖨

Combinatie

1. \(\left\{\begin{matrix}-6x+6y=-12\\7y-8x=-21\end{matrix}\right.\)
2. \(\left\{\begin{matrix}10y=20+10x\\5x-3y=10\end{matrix}\right.\)
3. \(\left\{\begin{matrix}-9y=63-3x\\-5x+5y=-15\end{matrix}\right.\)
4. \(\left\{\begin{matrix}4y-5x=34\\-10x+3y=88\end{matrix}\right.\)
5. \(\left\{\begin{matrix}-4x-9y=76\\10y+10x=-90\end{matrix}\right.\)
6. \(\left\{\begin{matrix}6y=-28+4x\\10x-9y=46\end{matrix}\right.\)
7. \(\left\{\begin{matrix}-4x-10y=6\\2x-8y=36\end{matrix}\right.\)
8. \(\left\{\begin{matrix}-6x+9y=-63\\9x=-10y+24\end{matrix}\right.\)
9. \(\left\{\begin{matrix}-10x-6y=76\\-5y+5x=-70\end{matrix}\right.\)
10. \(\left\{\begin{matrix}3x-3y=33\\-2x+7y=-32\end{matrix}\right.\)
11. \(\left\{\begin{matrix}8x+3y=-80\\-7x-4y=81\end{matrix}\right.\)
12. \(\left\{\begin{matrix}-5x+7y=54\\-3x=5y+14\end{matrix}\right.\)

---

Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}-6x+6y=-12\\7y-8x=-21\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+6y=-12\\-8x+7y=-21\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+6y=-12& \color{red}{4.} & \color{blue}{7.} \\-8x+7y=-21& \color{red}{-3.} & \color{blue}{-6.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-24x+24x}+24y-21y=-48+63} \\ \color{blue}{-42x+48x\underline{+42y-42y}=-84+126} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3y=15 \\6x=42\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{15}{3}=5 \\x=\frac{42}{6}=7\end{matrix}\right.\\ \qquad V=\{(7,5)\}\)
2. \(\left\{\begin{matrix}10y=20+10x\\5x-3y=10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x+10y=20\\5x-3y=10\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x+10y=20& \color{red}{1.} & \color{blue}{3.} \\5x-3y=10& \color{red}{2.} & \color{blue}{10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}+10y-6y=20+20} \\ \color{blue}{-30x+50x\underline{+30y-30y}=60+100} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4y=40 \\20x=160\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{40}{4}=10 \\x=\frac{160}{20}=8\end{matrix}\right.\\ \qquad V=\{(8,10)\}\)
3. \(\left\{\begin{matrix}-9y=63-3x\\-5x+5y=-15\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x-9y=63\\-5x+5y=-15\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-9y=63& \color{red}{5.} & \color{blue}{5.} \\-5x+5y=-15& \color{red}{3.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{15x-15x}-45y+15y=315-45} \\ \color{blue}{15x-45x\underline{-45y+45y}=315-135} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-30y=270 \\-30x=180\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{270}{-30}=-9 \\x=\frac{180}{-30}=-6\end{matrix}\right.\\ \qquad V=\{(-6,-9)\}\)
4. \(\left\{\begin{matrix}4y-5x=34\\-10x+3y=88\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+4y=34\\-10x+3y=88\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x+4y=34& \color{red}{2.} & \color{blue}{3.} \\-10x+3y=88& \color{red}{-1.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}+8y-3y=68-88} \\ \color{blue}{-15x+40x\underline{+12y-12y}=102-352} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5y=-20 \\25x=-250\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-20}{5}=-4 \\x=\frac{-250}{25}=-10\end{matrix}\right.\\ \qquad V=\{(-10,-4)\}\)
5. \(\left\{\begin{matrix}-4x-9y=76\\10y+10x=-90\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x-9y=76\\10x+10y=-90\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x-9y=76& \color{red}{5.} & \color{blue}{10.} \\10x+10y=-90& \color{red}{2.} & \color{blue}{9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-20x+20x}-45y+20y=380-180} \\ \color{blue}{-40x+90x\underline{-90y+90y}=760-810} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-25y=200 \\50x=-50\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{200}{-25}=-8 \\x=\frac{-50}{50}=-1\end{matrix}\right.\\ \qquad V=\{(-1,-8)\}\)
6. \(\left\{\begin{matrix}6y=-28+4x\\10x-9y=46\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+6y=-28\\10x-9y=46\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x+6y=-28& \color{red}{5.} & \color{blue}{3.} \\10x-9y=46& \color{red}{2.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-20x+20x}+30y-18y=-140+92} \\ \color{blue}{-12x+20x\underline{+18y-18y}=-84+92} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}12y=-48 \\8x=8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-48}{12}=-4 \\x=\frac{8}{8}=1\end{matrix}\right.\\ \qquad V=\{(1,-4)\}\)
7. \(\left\{\begin{matrix}-4x-10y=6\\2x-8y=36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x-10y=6& \color{red}{1.} & \color{blue}{4.} \\2x-8y=36& \color{red}{2.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-4x+4x}-10y-16y=6+72} \\ \color{blue}{-16x-10x\underline{-40y+40y}=24-180} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-26y=78 \\-26x=-156\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{78}{-26}=-3 \\x=\frac{-156}{-26}=6\end{matrix}\right.\\ \qquad V=\{(6,-3)\}\)
8. \(\left\{\begin{matrix}-6x+9y=-63\\9x=-10y+24\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+9y=-63\\9x+10y=24\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+9y=-63& \color{red}{3.} & \color{blue}{10.} \\9x+10y=24& \color{red}{2.} & \color{blue}{-9.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}+27y+20y=-189+48} \\ \color{blue}{-60x-81x\underline{+90y-90y}=-630-216} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}47y=-141 \\-141x=-846\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-141}{47}=-3 \\x=\frac{-846}{-141}=6\end{matrix}\right.\\ \qquad V=\{(6,-3)\}\)
9. \(\left\{\begin{matrix}-10x-6y=76\\-5y+5x=-70\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x-6y=76\\5x-5y=-70\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x-6y=76& \color{red}{1.} & \color{blue}{5.} \\5x-5y=-70& \color{red}{2.} & \color{blue}{-6.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}-6y-10y=76-140} \\ \color{blue}{-50x-30x\underline{-30y+30y}=380+420} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-16y=-64 \\-80x=800\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-64}{-16}=4 \\x=\frac{800}{-80}=-10\end{matrix}\right.\\ \qquad V=\{(-10,4)\}\)
10. \(\left\{\begin{matrix}3x-3y=33\\-2x+7y=-32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}3x-3y=33& \color{red}{2.} & \color{blue}{7.} \\-2x+7y=-32& \color{red}{3.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}-6y+21y=66-96} \\ \color{blue}{21x-6x\underline{-21y+21y}=231-96} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}15y=-30 \\15x=135\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-30}{15}=-2 \\x=\frac{135}{15}=9\end{matrix}\right.\\ \qquad V=\{(9,-2)\}\)
11. \(\left\{\begin{matrix}8x+3y=-80\\-7x-4y=81\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x+3y=-80& \color{red}{7.} & \color{blue}{4.} \\-7x-4y=81& \color{red}{8.} & \color{blue}{3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{56x-56x}+21y-32y=-560+648} \\ \color{blue}{32x-21x\underline{+12y-12y}=-320+243} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-11y=88 \\11x=-77\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{88}{-11}=-8 \\x=\frac{-77}{11}=-7\end{matrix}\right.\\ \qquad V=\{(-7,-8)\}\)
12. \(\left\{\begin{matrix}-5x+7y=54\\-3x=5y+14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-5x+7y=54\\-3x-5y=14\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-5x+7y=54& \color{red}{3.} & \color{blue}{5.} \\-3x-5y=14& \color{red}{-5.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-15x+15x}+21y+25y=162-70} \\ \color{blue}{-25x-21x\underline{+35y-35y}=270+98} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}46y=92 \\-46x=368\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{92}{46}=2 \\x=\frac{368}{-46}=-8\end{matrix}\right.\\ \qquad V=\{(-8,2)\}\)