Question

Determine the number of solutions for the system of equations

y = 5x + 4

y = 5x - 2


Infinitely many solutions

No solution

Two solutions

One solution

Answer 1

To determine the number of solutions for the given system of equations, we can analyze the equations:

1. \( y = 5x + 4 \)
2. \( y = 5x - 2 \)

Both equations are in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

- The first equation has a slope of 5 and a y-intercept of 4.
- The second equation has the same slope of 5 but a different y-intercept of -2.

Since both equations have the same slope (5), they are parallel lines. Parallel lines do not intersect. Therefore, they have no points in common.

As a result, the system of equations has:

**No solution**.