Bài 1:
\(b,\text{PT hoành độ giao điểm: }-2x+5=5x-2\Leftrightarrow x=1\Leftrightarrow y=3\Leftrightarrow E\left(1;3\right)\\ c,\Leftrightarrow\left(d_3\right)\text{//}\left(d_2\right)\Leftrightarrow a=5;b\ne-2\\ \Leftrightarrow\left(d_3\right):y=5x+b\\ \left(d_3\right)\cap\left(d_1\right)\text{ trên }Oy\Leftrightarrow y=-2x+5=0\Leftrightarrow x=\dfrac{5}{2}\\ \Leftrightarrow5\cdot\dfrac{5}{2}+b=0\\ \Leftrightarrow b=-\dfrac{25}{2}\\ \Leftrightarrow\left(d_3\right):y=5x-\dfrac{25}{2}\)
Bài 2:
\(a,\Leftrightarrow\left\{{}\begin{matrix}a+b=2\\3a+b=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2a=-1\\a+b=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=-\dfrac{1}{2}\\b=\dfrac{5}{2}\end{matrix}\right.\\ b,\left(d\right):y=-\dfrac{1}{2}x+\dfrac{5}{2}\\ \text{Gọi góc tạo bởi }\left(d\right)\text{ và }Ox\text{ là }\alpha\\ \text{Vì }-\dfrac{1}{2}< 0\Leftrightarrow\alpha>90^0\\ \text{Hệ số góc: }\dfrac{1}{2}\\ \Leftrightarrow\tan\left(180^0-\alpha\right)=\dfrac{1}{2}\approx27^0\\ \Leftrightarrow\alpha\approx180^0-27^0=153^0\)
