Determine the number of solutions to this system of linear equations: y=7x−3 y=7x+3

1 answer

To determine the number of solutions to the system of equations given by:

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

we start by observing the structure of the equations. Both equations are in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

  • The slope of the first equation \( y = 7x - 3 \) is \( 7 \), and its y-intercept is \( -3 \).
  • The slope of the second equation \( y = 7x + 3 \) is also \( 7 \), but its y-intercept is \( 3 \).

Since the slopes of both lines are equal (both are \( 7 \)), the lines are parallel. Parallel lines do not intersect, which means they have no points in common.

Therefore, the number of solutions to the system of equations is:

\[ \boxed{0} \]