Substitutie
\(\left\{\begin{matrix}4x+2y=46\\-x=-4y+20\end{matrix}\right.\)
\(\left\{\begin{matrix}4x+2y=46\\-x=-4y+20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}4x+2y=46\\-x+4y=20\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}4x+2y=46\\ 4y-20=x\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}4\left(4y-20\right)+2y=46\\x=4y-20\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}16y-80+2y=46\\x=4y-20\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}18y=46+80=126\\x=4y-20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{126}{18} = 7 \\ x=4y-20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 7 \\ x=4.(7)-20=8\end{matrix}\right.\\ \qquad V=\{(8,7)\}\)
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vanhoeckes.be/wiskunde 2025-05-31 06:14:00