Question

How many solutions does the system have? \begin{cases} 5y =15x-40 \\\\ y = 3x-8 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ 5y=15x−40 y=3x−8 ​ Choose 1 answer: Choose 1 answer: (Choice A) A Exactly one solution (Choice B) B No solutions (Choice C) C Infinitely many solutions

Answer 1

Answer:

(C) Infinitely many solutions

Step-by-step explanation:

Converting the lines into the from $ax+by+c=0$

$5y=15x-40\\\Rightarrow 15x-5y-40=0$

$y=3x-8\\\Rightarrow 3x-y-8=0$

$\dfrac{a_1}{a_2}=\dfrac{15}{3}=5$

$\dfrac{b_1}{b_2}=\dfrac{-5}{-1}=5$

$\dfrac{c_1}{c_2}=\dfrac{-40}{-8}=5$

So, $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$.

Hence, these lines have infinitely many solutions.