Tell whether the system has one solution, infinitely many solutions, or no solution.

6y=-5x+24
2.5x+3y=12

A.
One solution

B.
Infinitely many solutions

C.
No solution

I'll be glad to check your answer.

note that you can rewrite the 1st line as

5x+6y = 24
how does that relate to the 2nd equation?

6y = -5x + 24.

5x + 6y = 24, Divide both sides by 2:
Eq1: 2.5x + 3y = 12.

Eq2: 2.5x + 3y = 12.
So Eq1 and Eq2 are the same.

To determine whether the system of equations has one solution, infinitely many solutions, or no solution, we can solve the system using one of the methods, such as substitution or elimination.

Given the system of equations:

6y = -5x + 24 (Equation 1)
2.5x + 3y = 12 (Equation 2)

Let's solve the system using the elimination method:

First, let's multiply Equation 2 by 2 to make the coefficients of x in both equations the same:

2(2.5x + 3y) = 2(12)
5x + 6y = 24 (Equation 3)

Now, we have the following system:

6y = -5x + 24 (Equation 1)
5x + 6y = 24 (Equation 3)

To eliminate the y term, we can multiply Equation 1 by 6 and Equation 3 by 5:

6(6y) = 6(-5x + 24)
36y = -30x + 144 (Equation 4)

5(5x + 6y) = 5(24)
25x + 30y = 120 (Equation 5)

Now, we have the following system:

36y = -30x + 144 (Equation 4)
25x + 30y = 120 (Equation 5)

To eliminate the y term, we can multiply Equation 4 by 5 and Equation 5 by 6:

5(36y) = 5(-30x + 144)
180y = -150x + 720 (Equation 6)

6(25x + 30y) = 6(120)
150x + 180y = 720 (Equation 7)

Now, we have the following system:

180y = -150x + 720 (Equation 6)
150x + 180y = 720 (Equation 7)

Since both Equation 6 and Equation 7 are the same, this means they represent the same line. This indicates that the system of equations has infinitely many solutions.

Therefore, the correct answer is B. Infinitely many solutions.