How many solutions does the system have? 5y = 15x - 40
y = 3x -8
A. Infinitely many solutions
B. No solutions
C. Exactly one solution

A; infinitely many solutions

Step-by-step explanation:

first, let's simplify the first equation to make it simpler.

divide both sides by 5

y=3x-8

new system

y=3x-8

y=3x-8

as you can see, they are the same.

not mandatory but useful!⬇⬇⬇⬇

just to be more clear, let's substitute them. since they're both already in y=, we can make them both set to each other.

3x-8=3x-8

add 8 to both sides; subtract 3x from one side

0=0

the answer is A, Infinitely many solutions.

hope this helped <3333333

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: