Stelsels

Werk uit

\(\left\{\begin{matrix}y=-18+6x\\5x+5y=-20\end{matrix}\right.\)

\(\left\{\begin{matrix}y=-18+6x\\5x+5y=-20\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-6x+y=-18\\5x+5y=-20\end{matrix}\right.\text{(Niet verplichte stap, proper schrijven)}\\ \Leftrightarrow \left\{\begin{matrix}y=6x-18\\ 5x+5y=-20\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}y=6x-18\\ 5x+5\left(6x-18\right)=-20\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}y=6x-18\\ 5x+30x-90=-20\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}y=6x-18\\ 35x=-20+90=70\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=6x-18\\ x=\frac{70}{35}=2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y=6.(2)-18=-6\\ x=2\end{matrix}\right.\\ \qquad V=\{(2,-6)\}\)