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

(C) Infinitely many solutions

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`

`(a_1)/(a_2)=(15)/(3)=5`

`(b_1)/(b_2)=(-5)/(-1)=5`

`(c_1)/(c_2)=(-40)/(-8)=5`

So,
`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)`.

Hence, these lines have infinitely many solutions.