Stelsels substitutie

Substitutie

\(\left\{\begin{matrix}-2x-5y=5\\x+4y=2\end{matrix}\right.\)

\(\left\{\begin{matrix}-2x-5y=5\\x+4y=2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-2x-5y=5\\ x=-4y+2\end{matrix}\right.\text{(Afzonderen onbekende met coëff. 1)}\\ \Leftrightarrow \left\{\begin{matrix}-2\left(-4y+2\right)-5y=5\\x=-4y+2\end{matrix}\right.\text{(Substitutie!)}\\ \Leftrightarrow \left\{\begin{matrix}8y-4-5y=5\\x=-4y+2\end{matrix}\right.\text{(Distributie)}\\ \Leftrightarrow \left\{\begin{matrix}3y=5+4=9\\x=-4y+2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = \frac{9}{3} = 3 \\ x=-4y+2\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}y = 3 \\ x=-4.(3)+2=-10\end{matrix}\right.\\ \qquad V=\{(-10,3)\}\)