Question

in reperul cartezian xOy se cinsidera dreptele d1 :2x-y-1=0 si d2:x+2y-3=0.Aflati coordonatele punctului de intersectie a dreptelor d1 si d2.

Answer 1

$d_1:2x-y-1=0.\\ d_2:x+2y-3=0.\\ \\ Faci~sistem~din~astea~2:\\ \\ \begin{cases}~2x-y-1=0\\~x+2y-3=0~\end{cases}~\Leftrightarrow~\begin{cases}~x=\frac{y+1}{2} \\~\frac{y+1}{2}+2y=3~\end{cases}~\Leftrightarrow~\begin{cases}~x=\frac{y+1}{2}\\~y=1~\end{cases}~\Leftrightarrow~\begin{cases}~x=1\\~y=1~\end{cases}\\ \\ \\Deci,~punctul~de~intersectie~al~dreptelor~este~\boxed{{M(1,1)}}$