To solve the given system of equations by elimination, we first rewrite the equations clearly. The system can be expressed as:
- \( 6x + 18y = 24 \)
- \( 15y - 20 = -5x \)
We can rearrange the second equation for clarity:
\[ 5x + 15y = 20 \]
Now we have the system:
- \( 6x + 18y = 24 \)
- \( 5x + 15y = 20 \)
Next, we can use elimination to solve the equations. We will make the coefficients of \( x \) or \( y \) the same in both equations. Let's eliminate \( x \).
To do this, we can multiply the first equation by 5 and the second equation by 6:
\[ 5(6x + 18y) = 5(24) \implies 30x + 90y = 120 \] \[ 6(5x + 15y) = 6(20) \implies 30x + 90y = 120 \]
Now we have:
- \( 30x + 90y = 120 \)
- \( 30x + 90y = 120 \)
Since both equations are identical, it means that they represent the same line. Therefore, there are infinitely many solutions along that line.
So the answer is:
B. There are infinitely many solutions.