Substitutie
\(\left\{\begin{matrix}3x+2y=2\\5x=-y+8\end{matrix}\right.\)
\(\left\{\begin{matrix}3x+2y=2\\5x=-y+8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}3x+2y=2\\5x+y=8\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}3x+2y=2\\ y=-5x+8\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}3x+2\left(-5x+8\right)=2\\y=-5x+8\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}3x-10x+16=2\\y=-5x+8\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-7x=2-16=-14\\y=-5x+8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = \frac{-14}{-7} = 2 \\ y=-5x+8\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x = 2 \\ y=-5.(2)+8=-2\end{matrix}\right.\\ \qquad V=\{(2,-2)\}\)
Oefeningengenerator
wiskundeoefeningen.be 2026-09-19 09:16:33 Een site van Busleyden Atheneum Mechelen