Question

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**.