Question

"How many solutions does the system have?

4x−6y=−24
2x−3y=−6

Choose one answer:

A) Exactly one solution
B) No solutions
C) Infinitely many solutions"

Answer 1

The given system of equations represents the same line as the two equations are multiples of each other, which means there are infinitely many solutions.

Step-by-step explanation:

To determine how many solutions the system of linear equations has, we can compare their coefficients. If we take the given system:

1. 4x − 6y = − 24
2. 2x − 3y = − 6

We notice that the second equation is exactly half of the first. That is:

1/2 (4x − 6y) = 1/2 (− 24)

which simplifies to:

2x − 3y = − 6

Since the two equations are multiples of each other, they represent the same line. Therefore, there are infinitely many solutions because every point on the line is a solution to both equations. Hence, the correct answer is C) Infinitely many solutions.