Substitutie
\(\left\{\begin{matrix}-5y=-50+x\\5x-3y=-2\end{matrix}\right.\)
\(\left\{\begin{matrix}-5y=-50+x\\5x-3y=-2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-x-5y=-50\\5x-3y=-2\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-5y+50=x\\5x-3y=-2\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}x=-5y+50\\ 5.\left(-5y+50\right)-3y=-2\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}x=-5y+50\\ -25y+250-3y=-2\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}x=-5y+50\\ -28y=-2-250=-252\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-5y+50\\ y=\frac{-252}{-28}=9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x=-5.(9)+50=5\\ y=9\end{matrix}\right.\\ \qquad V=\{(5,9)\}\)
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vanhoeckes.be/wiskunde 2024-05-02 10:49:41