Consider the system of linear equation:
[tex]\left\{\begin{array}{l}a_1x+b_1y=c_1\\a_2x+b_2y=c_2\end{array}\right.[/tex]
This system will have:
- exactly one solution if [tex]\dfrac{a_1}{a_2}\neq \dfrac{b_1}{b_2};[/tex]
- no solutions if [tex]\dfrac{a_1}{a_2}= \dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2};[/tex]
- infinetely many solutions if [tex]\dfrac{a_1}{a_2}= \dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}.[/tex]
If a system of linear equations consists of two lines that are exactly the same ([tex]a_1x+b_1y=c_1[/tex]), then [tex]\dfrac{a_1}{a_1}= \dfrac{b_1}{b_1}=\dfrac{c_1}{c_1}=1[/tex] and the system will have infinitely many solutions.
Answer: correct choice is D.
