does y = 5x + 7 3y - 15x = 18 have one solution, no solution, or infinite solutions

Answer 1

To determine whether the system of equations

1. \( y = 5x + 7 \)
2. \( 3y - 15x = 18 \)

has one solution, no solution, or infinitely many solutions, we can simplify the second equation and see if it is consistent with the first.

First, substitute \( y \) from the first equation into the second equation:

1. Substitute \( y \) in the second equation:

   \[ 3(5x + 7) - 15x = 18 \]

   Expanding this gives:

   \[ 15x + 21 - 15x = 18 \]

   The \( 15x \) terms cancel out:

   \[ 21 = 18 \]

This is a false statement (21 does not equal 18), which indicates that the two equations are inconsistent.

Thus, the system of equations has no solution.