Stelsels combinatie

Hoofdmenu Eentje per keer  🖨

Combinatie

1. \(\left\{\begin{matrix}-5y=-25-5x\\9x+7y=83\end{matrix}\right.\)
2. \(\left\{\begin{matrix}-3x+7y=-36\\-6x=10y+144\end{matrix}\right.\)
3. \(\left\{\begin{matrix}-2y=74-6x\\-7x+6y=-123\end{matrix}\right.\)
4. \(\left\{\begin{matrix}6y=30+4x\\10x-7y=-3\end{matrix}\right.\)
5. \(\left\{\begin{matrix}-6x+6y=-12\\10y-5x=25\end{matrix}\right.\)
6. \(\left\{\begin{matrix}-2y=10+2x\\9x-5y=-31\end{matrix}\right.\)
7. \(\left\{\begin{matrix}-10x+6y=-124\\10y+2x=-76\end{matrix}\right.\)
8. \(\left\{\begin{matrix}-2y+2x=8\\2x-3y=10\end{matrix}\right.\)
9. \(\left\{\begin{matrix}6x+2y=-54\\-6x+5y=33\end{matrix}\right.\)
10. \(\left\{\begin{matrix}-7x+6y=-43\\9x+2y=65\end{matrix}\right.\)
11. \(\left\{\begin{matrix}6x-4y=-88\\-7x-9y=7\end{matrix}\right.\)
12. \(\left\{\begin{matrix}6x+8y=-92\\10x-7y=-11\end{matrix}\right.\)

---

Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}-5y=-25-5x\\9x+7y=83\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}5x-5y=-25\\9x+7y=83\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-5y=-25& \color{red}{9.} & \color{blue}{7.} \\9x+7y=83& \color{red}{-5.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{45x-45x}-45y-35y=-225-415} \\ \color{blue}{35x+45x\underline{-35y+35y}=-175+415} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-80y=-640 \\80x=240\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-640}{-80}=8 \\x=\frac{240}{80}=3\end{matrix}\right.\\ \qquad V=\{(3,8)\}\)
2. \(\left\{\begin{matrix}-3x+7y=-36\\-6x=10y+144\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+7y=-36\\-6x-10y=144\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+7y=-36& \color{red}{2.} & \color{blue}{10.} \\-6x-10y=144& \color{red}{-1.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-6x+6x}+14y+10y=-72-144} \\ \color{blue}{-30x-42x\underline{+70y-70y}=-360+1008} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}24y=-216 \\-72x=648\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-216}{24}=-9 \\x=\frac{648}{-72}=-9\end{matrix}\right.\\ \qquad V=\{(-9,-9)\}\)
3. \(\left\{\begin{matrix}-2y=74-6x\\-7x+6y=-123\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x-2y=74\\-7x+6y=-123\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-2y=74& \color{red}{7.} & \color{blue}{3.} \\-7x+6y=-123& \color{red}{6.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{42x-42x}-14y+36y=518-738} \\ \color{blue}{18x-7x\underline{-6y+6y}=222-123} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}22y=-220 \\11x=99\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-220}{22}=-10 \\x=\frac{99}{11}=9\end{matrix}\right.\\ \qquad V=\{(9,-10)\}\)
4. \(\left\{\begin{matrix}6y=30+4x\\10x-7y=-3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+6y=30\\10x-7y=-3\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x+6y=30& \color{red}{5.} & \color{blue}{7.} \\10x-7y=-3& \color{red}{2.} & \color{blue}{6.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-20x+20x}+30y-14y=150-6} \\ \color{blue}{-28x+60x\underline{+42y-42y}=210-18} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}16y=144 \\32x=192\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{144}{16}=9 \\x=\frac{192}{32}=6\end{matrix}\right.\\ \qquad V=\{(6,9)\}\)
5. \(\left\{\begin{matrix}-6x+6y=-12\\10y-5x=25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+6y=-12\\-5x+10y=25\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x+6y=-12& \color{red}{5.} & \color{blue}{5.} \\-5x+10y=25& \color{red}{-6.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}+30y-60y=-60-150} \\ \color{blue}{-30x+15x\underline{+30y-30y}=-60-75} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-30y=-210 \\-15x=-135\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-210}{-30}=7 \\x=\frac{-135}{-15}=9\end{matrix}\right.\\ \qquad V=\{(9,7)\}\)
6. \(\left\{\begin{matrix}-2y=10+2x\\9x-5y=-31\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-2y=10\\9x-5y=-31\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x-2y=10& \color{red}{9.} & \color{blue}{5.} \\9x-5y=-31& \color{red}{2.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-18x+18x}-18y-10y=90-62} \\ \color{blue}{-10x-18x\underline{-10y+10y}=50+62} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-28y=28 \\-28x=112\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{28}{-28}=-1 \\x=\frac{112}{-28}=-4\end{matrix}\right.\\ \qquad V=\{(-4,-1)\}\)
7. \(\left\{\begin{matrix}-10x+6y=-124\\10y+2x=-76\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x+6y=-124\\2x+10y=-76\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x+6y=-124& \color{red}{1.} & \color{blue}{5.} \\2x+10y=-76& \color{red}{5.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}+6y+50y=-124-380} \\ \color{blue}{-50x-6x\underline{+30y-30y}=-620+228} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}56y=-504 \\-56x=-392\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-504}{56}=-9 \\x=\frac{-392}{-56}=7\end{matrix}\right.\\ \qquad V=\{(7,-9)\}\)
8. \(\left\{\begin{matrix}-2y+2x=8\\2x-3y=10\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x-2y=8\\2x-3y=10\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x-2y=8& \color{red}{1.} & \color{blue}{3.} \\2x-3y=10& \color{red}{-1.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{2x-2x}-2y+3y=8-10} \\ \color{blue}{6x-4x\underline{-6y+6y}=24-20} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=-2 \\2x=4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-2}{1}=-2 \\x=\frac{4}{2}=2\end{matrix}\right.\\ \qquad V=\{(2,-2)\}\)
9. \(\left\{\begin{matrix}6x+2y=-54\\-6x+5y=33\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x+2y=-54& \color{red}{1.} & \color{blue}{5.} \\-6x+5y=33& \color{red}{1.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}+2y+5y=-54+33} \\ \color{blue}{30x+12x\underline{+10y-10y}=-270-66} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7y=-21 \\42x=-336\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-21}{7}=-3 \\x=\frac{-336}{42}=-8\end{matrix}\right.\\ \qquad V=\{(-8,-3)\}\)
10. \(\left\{\begin{matrix}-7x+6y=-43\\9x+2y=65\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x+6y=-43& \color{red}{9.} & \color{blue}{1.} \\9x+2y=65& \color{red}{7.} & \color{blue}{-3.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-63x+63x}+54y+14y=-387+455} \\ \color{blue}{-7x-27x\underline{+6y-6y}=-43-195} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}68y=68 \\-34x=-238\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{68}{68}=1 \\x=\frac{-238}{-34}=7\end{matrix}\right.\\ \qquad V=\{(7,1)\}\)
11. \(\left\{\begin{matrix}6x-4y=-88\\-7x-9y=7\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-4y=-88& \color{red}{7.} & \color{blue}{9.} \\-7x-9y=7& \color{red}{6.} & \color{blue}{-4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{42x-42x}-28y-54y=-616+42} \\ \color{blue}{54x+28x\underline{-36y+36y}=-792-28} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-82y=-574 \\82x=-820\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-574}{-82}=7 \\x=\frac{-820}{82}=-10\end{matrix}\right.\\ \qquad V=\{(-10,7)\}\)
12. \(\left\{\begin{matrix}6x+8y=-92\\10x-7y=-11\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x+8y=-92& \color{red}{5.} & \color{blue}{7.} \\10x-7y=-11& \color{red}{-3.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}+40y+21y=-460+33} \\ \color{blue}{42x+80x\underline{+56y-56y}=-644-88} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}61y=-427 \\122x=-732\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-427}{61}=-7 \\x=\frac{-732}{122}=-6\end{matrix}\right.\\ \qquad V=\{(-6,-7)\}\)