Substitutie
\(\left\{\begin{matrix}-4y=-38-2x\\x-3y=-27\end{matrix}\right.\)
\(\left\{\begin{matrix}-4y=-38-2x\\x-3y=-27\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}2x-4y=-38\\x-3y=-27\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}2x-4y=-38\\ x=3y-27\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}2\left(3y-27\right)-4y=-38\\x=3y-27\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}6y-54-4y=-38\\x=3y-27\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}2y=-38+54=16\\x=3y-27\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{16}{2} = 8 \\ x=3y-27\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 8 \\ x=3.(8)-27=-3\end{matrix}\right.\\ \qquad V=\{(-3,8)\}\)
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vanhoeckes.be/wiskunde 2026-03-07 03:24:56