Stelsels combinatie

Combinatie

1. $$\left\{\begin{matrix}-4x+5y=41\\2y+4x=-6\end{matrix}\right.$$
2. $$\left\{\begin{matrix}7x+3y=-32\\6y+5x=-46\end{matrix}\right.$$
3. $$\left\{\begin{matrix}4x-4y=-68\\-6y-9x=18\end{matrix}\right.$$
4. $$\left\{\begin{matrix}-6x-4y=-26\\-10x+7y=25\end{matrix}\right.$$
5. $$\left\{\begin{matrix}-2x+2y=-24\\-5x-10y=75\end{matrix}\right.$$
6. $$\left\{\begin{matrix}7y=68-2x\\8x+3y=72\end{matrix}\right.$$
7. $$\left\{\begin{matrix}2y-10x=-24\\-5x+3y=4\end{matrix}\right.$$
8. $$\left\{\begin{matrix}6x+2y=54\\-5x=-7y+7\end{matrix}\right.$$
9. $$\left\{\begin{matrix}7x-7y=-35\\10y+9x=12\end{matrix}\right.$$
10. $$\left\{\begin{matrix}3y+6x=39\\-2x+9y=77\end{matrix}\right.$$
11. $$\left\{\begin{matrix}-7x+2y=-60\\6x=-7y+34\end{matrix}\right.$$
12. $$\left\{\begin{matrix}2x-8y=4\\-4y+4x=32\end{matrix}\right.$$

Combinatie

Verbetersleutel

1. $$\left\{\begin{matrix}-4x+5y=41\\2y+4x=-6\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4x+5y=41\\4x+2y=-6\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-4x+5y=41& \color{red}{1.} & \color{blue}{2.} \\4x+2y=-6& \color{red}{1.} & \color{blue}{-5.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-4x+4x}+5y+2y=41-6} \\ \color{blue}{-8x-20x\underline{+10y-10y}=82+30} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7y=35 \\-28x=112\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{35}{7}=5 \\x=\frac{112}{-28}=-4\end{matrix}\right.\\ \qquad V=\{(-4,5)\}$$
2. $$\left\{\begin{matrix}7x+3y=-32\\6y+5x=-46\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x+3y=-32\\5x+6y=-46\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x+3y=-32& \color{red}{5.} & \color{blue}{2.} \\5x+6y=-46& \color{red}{-7.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{35x-35x}+15y-42y=-160+322} \\ \color{blue}{14x-5x\underline{+6y-6y}=-64+46} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-27y=162 \\9x=-18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{162}{-27}=-6 \\x=\frac{-18}{9}=-2\end{matrix}\right.\\ \qquad V=\{(-2,-6)\}$$
3. $$\left\{\begin{matrix}4x-4y=-68\\-6y-9x=18\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x-4y=-68\\-9x-6y=18\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}4x-4y=-68& \color{red}{9.} & \color{blue}{3.} \\-9x-6y=18& \color{red}{4.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{36x-36x}-36y-24y=-612+72} \\ \color{blue}{12x+18x\underline{-12y+12y}=-204-36} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-60y=-540 \\30x=-240\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-540}{-60}=9 \\x=\frac{-240}{30}=-8\end{matrix}\right.\\ \qquad V=\{(-8,9)\}$$
4. $$\left\{\begin{matrix}-6x-4y=-26\\-10x+7y=25\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-6x-4y=-26& \color{red}{5.} & \color{blue}{7.} \\-10x+7y=25& \color{red}{-3.} & \color{blue}{4.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-30x+30x}-20y-21y=-130-75} \\ \color{blue}{-42x-40x\underline{-28y+28y}=-182+100} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-41y=-205 \\-82x=-82\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-205}{-41}=5 \\x=\frac{-82}{-82}=1\end{matrix}\right.\\ \qquad V=\{(1,5)\}$$
5. $$\left\{\begin{matrix}-2x+2y=-24\\-5x-10y=75\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-2x+2y=-24& \color{red}{5.} & \color{blue}{5.} \\-5x-10y=75& \color{red}{-2.} & \color{blue}{1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}+10y+20y=-120-150} \\ \color{blue}{-10x-5x\underline{+10y-10y}=-120+75} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}30y=-270 \\-15x=-45\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-270}{30}=-9 \\x=\frac{-45}{-15}=3\end{matrix}\right.\\ \qquad V=\{(3,-9)\}$$
6. $$\left\{\begin{matrix}7y=68-2x\\8x+3y=72\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x+7y=68\\8x+3y=72\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x+7y=68& \color{red}{4.} & \color{blue}{3.} \\8x+3y=72& \color{red}{-1.} & \color{blue}{-7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{8x-8x}+28y-3y=272-72} \\ \color{blue}{6x-56x\underline{+21y-21y}=204-504} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}25y=200 \\-50x=-300\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{200}{25}=8 \\x=\frac{-300}{-50}=6\end{matrix}\right.\\ \qquad V=\{(6,8)\}$$
7. $$\left\{\begin{matrix}2y-10x=-24\\-5x+3y=4\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-10x+2y=-24\\-5x+3y=4\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-10x+2y=-24& \color{red}{1.} & \color{blue}{3.} \\-5x+3y=4& \color{red}{-2.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-10x+10x}+2y-6y=-24-8} \\ \color{blue}{-30x+10x\underline{+6y-6y}=-72-8} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-4y=-32 \\-20x=-80\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-32}{-4}=8 \\x=\frac{-80}{-20}=4\end{matrix}\right.\\ \qquad V=\{(4,8)\}$$
8. $$\left\{\begin{matrix}6x+2y=54\\-5x=-7y+7\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+2y=54\\-5x+7y=7\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x+2y=54& \color{red}{5.} & \color{blue}{7.} \\-5x+7y=7& \color{red}{6.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{30x-30x}+10y+42y=270+42} \\ \color{blue}{42x+10x\underline{+14y-14y}=378-14} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}52y=312 \\52x=364\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{312}{52}=6 \\x=\frac{364}{52}=7\end{matrix}\right.\\ \qquad V=\{(7,6)\}$$
9. $$\left\{\begin{matrix}7x-7y=-35\\10y+9x=12\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}7x-7y=-35\\9x+10y=12\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}7x-7y=-35& \color{red}{9.} & \color{blue}{10.} \\9x+10y=12& \color{red}{-7.} & \color{blue}{7.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{63x-63x}-63y-70y=-315-84} \\ \color{blue}{70x+63x\underline{-70y+70y}=-350+84} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-133y=-399 \\133x=-266\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-399}{-133}=3 \\x=\frac{-266}{133}=-2\end{matrix}\right.\\ \qquad V=\{(-2,3)\}$$
10. $$\left\{\begin{matrix}3y+6x=39\\-2x+9y=77\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}6x+3y=39\\-2x+9y=77\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}6x+3y=39& \color{red}{1.} & \color{blue}{3.} \\-2x+9y=77& \color{red}{3.} & \color{blue}{-1.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{6x-6x}+3y+27y=39+231} \\ \color{blue}{18x+2x\underline{+9y-9y}=117-77} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}30y=270 \\20x=40\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{270}{30}=9 \\x=\frac{40}{20}=2\end{matrix}\right.\\ \qquad V=\{(2,9)\}$$
11. $$\left\{\begin{matrix}-7x+2y=-60\\6x=-7y+34\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-7x+2y=-60\\6x+7y=34\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}-7x+2y=-60& \color{red}{6.} & \color{blue}{7.} \\6x+7y=34& \color{red}{7.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{-42x+42x}+12y+49y=-360+238} \\ \color{blue}{-49x-12x\underline{+14y-14y}=-420-68} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}61y=-122 \\-61x=-488\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-122}{61}=-2 \\x=\frac{-488}{-61}=8\end{matrix}\right.\\ \qquad V=\{(8,-2)\}$$
12. $$\left\{\begin{matrix}2x-8y=4\\-4y+4x=32\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x-8y=4\\4x-4y=32\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{array}{c|c|c}2x-8y=4& \color{red}{2.} & \color{blue}{1.} \\4x-4y=32& \color{red}{-1.} & \color{blue}{-2.} \end{array}\right.\\ \Leftrightarrow \left\{\begin{matrix} \color{red}{\underline{4x-4x}-16y+4y=8-32} \\ \color{blue}{2x-8x\underline{-8y+8y}=4-64} \end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-12y=-24 \\-6x=-60\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=\frac{-24}{-12}=2 \\x=\frac{-60}{-6}=10\end{matrix}\right.\\ \qquad V=\{(10,2)\}$$
Oefeningengenerator vanhoeckes.be/wiskunde 2024-08-09 04:32:04