Question

cho hai duong thang 

y=kx+(m-2) (d1)

y=(5-k)x+(4-m) ( d2)

voi dieu kien nao cua k va thi (d1) va (d2)

a) cat nhau  

b) song song

c) trung nhau

Answer 1

a)\(\left(d1\right)\) và \(\left(d2\right)\)cắt nhau 

\(\Leftrightarrow\hept{\begin{cases}5-k\ne k\\m-2=4-m\end{cases}}\Leftrightarrow\hept{\begin{cases}5=k+k\\m+m=4+2\end{cases}}\Leftrightarrow\hept{\begin{cases}2k\ne5\\2m=6\end{cases}}\Leftrightarrow\hept{\begin{cases}k\ne\frac{5}{2}\\m=3\end{cases}}\)  \(\Leftrightarrow m=3\)

b) \(\left(d1\right)\)và \(\left(d2\right)\)song song khi

\(\Leftrightarrow\hept{\begin{cases}5-k=k\\m-2\ne4-m\end{cases}}\Leftrightarrow\hept{\begin{cases}k=\frac{5}{2}\\m\ne3\end{cases}}\)

c) \(\left(d1\right)\)và \(\left(d2\right)\)trùng nhau 

\(\Leftrightarrow\hept{\begin{cases}5-k=k\\m-2=4-m\end{cases}}\Leftrightarrow\hept{\begin{cases}k=\frac{5}{2}\\m=3\end{cases}}\)