Toán Lớp 9: Tìm m để 3 đường thẳng $(d_{1}): y=mx-1; (d_{2}:y=(m-1)x+1;(d_{3}):y=2mx-3$ đồng quy
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Toán Lớp 9: Tìm m để 3 đường thẳng $(d_{1}): y=mx-1; (d_{2}:y=(m-1)x+1;(d_{3}):y=2mx-3$ đồng quy
Comments ( 1 )
mx – 1 = \left( {m – 1} \right).x + 1\\
\Leftrightarrow mx – 1 = mx – x + 1\\
\Leftrightarrow x = 1 + 1\\
\Leftrightarrow x = 2\\
\Leftrightarrow y = mx – 1 = m.2 – 1 = 2m – 1\\
\Leftrightarrow \left( {{d_1}} \right) \cap \left( {{d_2}} \right) = \left( {2;2m – 1} \right)
\end{array}$
\Leftrightarrow \left( {2;2m – 1} \right) \in {d_3}\\
\Leftrightarrow 2m – 1 = 2m.2 – 3\\
\Leftrightarrow 2m – 1 = 4m – 3\\
\Leftrightarrow 4m – 2m = – 1 + 3\\
\Leftrightarrow 2m = 2\\
\Leftrightarrow m = 1\\
Vay\,m = 1
\end{array}$