Stelsels combinatie

Hoofdmenu Eentje per keer  🖨

Combinatie

1. \(\left\{\begin{matrix}8x-7y=17\\3x=-5y+14\end{matrix}\right.\)
2. \(\left\{\begin{matrix}9x+2y=-90\\6x+8y=-120\end{matrix}\right.\)
3. \(\left\{\begin{matrix}6x-2y=-48\\5y-3x=36\end{matrix}\right.\)
4. \(\left\{\begin{matrix}-7x-7y=21\\2x+6y=22\end{matrix}\right.\)
5. \(\left\{\begin{matrix}10y-9x=103\\-4x+3y=40\end{matrix}\right.\)
6. \(\left\{\begin{matrix}-8y-6x=-10\\-10x+9y=162\end{matrix}\right.\)
7. \(\left\{\begin{matrix}5x-8y=80\\-7x+6y=-86\end{matrix}\right.\)
8. \(\left\{\begin{matrix}7y=91+3x\\9x+2y=-43\end{matrix}\right.\)
9. \(\left\{\begin{matrix}8x-5y=19\\-8y+4x=48\end{matrix}\right.\)
10. \(\left\{\begin{matrix}5y+4x=-32\\-10x-8y=44\end{matrix}\right.\)
11. \(\left\{\begin{matrix}4x-4y=32\\-3x=-2y-14\end{matrix}\right.\)
12. \(\left\{\begin{matrix}4x+8y=4\\-5x=5y+20\end{matrix}\right.\)

---

Combinatie

Verbetersleutel

1. \(\left\{\begin{matrix}8x-7y=17\\3x=-5y+14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x-7y=17\\3x+5y=14\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-7y=17& \color{red}{3.} & \color{blue}{5.} \\3x+5y=14& \color{red}{-8.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{24x-24x}-21y-40y=51-112} \\ \color{blue}{40x+21x\underline{-35y+35y}=85+98} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-61y=-61 \\61x=183\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-61}{-61}=1 \\x=\frac{183}{61}=3\end{matrix}\right.\\ \qquad V=\{(3,1)\}\)
2. \(\left\{\begin{matrix}9x+2y=-90\\6x+8y=-120\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}9x+2y=-90& \color{red}{2.} & \color{blue}{4.} \\6x+8y=-120& \color{red}{-3.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{18x-18x}+4y-24y=-180+360} \\ \color{blue}{36x-6x\underline{+8y-8y}=-360+120} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-20y=180 \\30x=-240\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{180}{-20}=-9 \\x=\frac{-240}{30}=-8\end{matrix}\right.\\ \qquad V=\{(-8,-9)\}\)
3. \(\left\{\begin{matrix}6x-2y=-48\\5y-3x=36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x-2y=-48\\-3x+5y=36\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x-2y=-48& \color{red}{1.} & \color{blue}{5.} \\-3x+5y=36& \color{red}{2.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}-2y+10y=-48+72} \\ \color{blue}{30x-6x\underline{-10y+10y}=-240+72} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8y=24 \\24x=-168\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{24}{8}=3 \\x=\frac{-168}{24}=-7\end{matrix}\right.\\ \qquad V=\{(-7,3)\}\)
4. \(\left\{\begin{matrix}-7x-7y=21\\2x+6y=22\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x-7y=21& \color{red}{2.} & \color{blue}{6.} \\2x+6y=22& \color{red}{7.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-14x+14x}-14y+42y=42+154} \\ \color{blue}{-42x+14x\underline{-42y+42y}=126+154} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}28y=196 \\-28x=280\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{196}{28}=7 \\x=\frac{280}{-28}=-10\end{matrix}\right.\\ \qquad V=\{(-10,7)\}\)
5. \(\left\{\begin{matrix}10y-9x=103\\-4x+3y=40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-9x+10y=103\\-4x+3y=40\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-9x+10y=103& \color{red}{4.} & \color{blue}{3.} \\-4x+3y=40& \color{red}{-9.} & \color{blue}{-10.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-36x+36x}+40y-27y=412-360} \\ \color{blue}{-27x+40x\underline{+30y-30y}=309-400} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}13y=52 \\13x=-91\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{52}{13}=4 \\x=\frac{-91}{13}=-7\end{matrix}\right.\\ \qquad V=\{(-7,4)\}\)
6. \(\left\{\begin{matrix}-8y-6x=-10\\-10x+9y=162\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x-8y=-10\\-10x+9y=162\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-8y=-10& \color{red}{5.} & \color{blue}{9.} \\-10x+9y=162& \color{red}{-3.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}-40y-27y=-50-486} \\ \color{blue}{-54x-80x\underline{-72y+72y}=-90+1296} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-67y=-536 \\-134x=1206\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-536}{-67}=8 \\x=\frac{1206}{-134}=-9\end{matrix}\right.\\ \qquad V=\{(-9,8)\}\)
7. \(\left\{\begin{matrix}5x-8y=80\\-7x+6y=-86\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}5x-8y=80& \color{red}{7.} & \color{blue}{3.} \\-7x+6y=-86& \color{red}{5.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{35x-35x}-56y+30y=560-430} \\ \color{blue}{15x-28x\underline{-24y+24y}=240-344} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-26y=130 \\-13x=-104\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{130}{-26}=-5 \\x=\frac{-104}{-13}=8\end{matrix}\right.\\ \qquad V=\{(8,-5)\}\)
8. \(\left\{\begin{matrix}7y=91+3x\\9x+2y=-43\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x+7y=91\\9x+2y=-43\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-3x+7y=91& \color{red}{3.} & \color{blue}{2.} \\9x+2y=-43& \color{red}{1.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-9x+9x}+21y+2y=273-43} \\ \color{blue}{-6x-63x\underline{+14y-14y}=182+301} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}23y=230 \\-69x=483\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{230}{23}=10 \\x=\frac{483}{-69}=-7\end{matrix}\right.\\ \qquad V=\{(-7,10)\}\)
9. \(\left\{\begin{matrix}8x-5y=19\\-8y+4x=48\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}8x-5y=19\\4x-8y=48\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}8x-5y=19& \color{red}{1.} & \color{blue}{8.} \\4x-8y=48& \color{red}{-2.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}-5y+16y=19-96} \\ \color{blue}{64x-20x\underline{-40y+40y}=152-240} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}11y=-77 \\44x=-88\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-77}{11}=-7 \\x=\frac{-88}{44}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-7)\}\)
10. \(\left\{\begin{matrix}5y+4x=-32\\-10x-8y=44\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+5y=-32\\-10x-8y=44\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+5y=-32& \color{red}{5.} & \color{blue}{8.} \\-10x-8y=44& \color{red}{2.} & \color{blue}{5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}+25y-16y=-160+88} \\ \color{blue}{32x-50x\underline{+40y-40y}=-256+220} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}9y=-72 \\-18x=-36\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-72}{9}=-8 \\x=\frac{-36}{-18}=2\end{matrix}\right.\\ \qquad V=\{(2,-8)\}\)
11. \(\left\{\begin{matrix}4x-4y=32\\-3x=-2y-14\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-4y=32\\-3x+2y=-14\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x-4y=32& \color{red}{3.} & \color{blue}{1.} \\-3x+2y=-14& \color{red}{4.} & \color{blue}{2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{12x-12x}-12y+8y=96-56} \\ \color{blue}{4x-6x\underline{-4y+4y}=32-28} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4y=40 \\-2x=4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{40}{-4}=-10 \\x=\frac{4}{-2}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-10)\}\)
12. \(\left\{\begin{matrix}4x+8y=4\\-5x=5y+20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+8y=4\\-5x-5y=20\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x+8y=4& \color{red}{5.} & \color{blue}{5.} \\-5x-5y=20& \color{red}{4.} & \color{blue}{8.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{20x-20x}+40y-20y=20+80} \\ \color{blue}{20x-40x\underline{+40y-40y}=20+160} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}20y=100 \\-20x=180\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{100}{20}=5 \\x=\frac{180}{-20}=-9\end{matrix}\right.\\ \qquad V=\{(-9,5)\}\)