Substitutie
\(\left\{\begin{matrix}-6x+4y=-46\\x=5y+51\end{matrix}\right.\)
\(\left\{\begin{matrix}-6x+4y=-46\\x=5y+51\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+4y=-46\\x-5y=51\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}-6x+4y=-46\\ x=5y+51\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-6\left(5y+51\right)+4y=-46\\x=5y+51\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}-30y-306+4y=-46\\x=5y+51\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}-26y=-46+306=260\\x=5y+51\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{260}{-26} = -10 \\ x=5y+51\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = -10 \\ x=5.(-10)+51=1\end{matrix}\right.\\ \qquad V=\{(1,-10)\}\)
Oefeningengenerator
wiskundeoefeningen.be 2025-09-17 17:29:09 Een site van Busleyden Atheneum Mechelen