How many solutions does the system have?12x−15y=184x−5y=6(1 point)Responsesno solutionno solutiontwo solutionstwo solutionsone solutionone solutioninfinitely many solutionsinfinitely many solutions

Answer 1

To determine how many solutions the given system of equations has, we will analyze the equations:

1. \( 12x - 15y = 18 \)
2. \( 4x - 5y = 6 \)

First, let's rewrite the first equation for clarity:

1. \( 12x - 15y = 18 \)
2. \( 4x - 5y = 6 \)

Notice that the second equation can be multiplied by 3 to see if it is a multiple of the first equation:

\[ 3(4x - 5y) = 3 \cdot 6 \]

That gives us:

\[ 12x - 15y = 18 \]

Now, we see that both equations are actually identical:

1. \( 12x - 15y = 18 \)
2. \( 12x - 15y = 18 \)

Since both equations represent the same line, there are infinitely many solutions to this system. Thus, the final answer is:

infinitely many solutions.