Question

Is the system of equations consistent and independent, consistent and dependent, or inconsistent?

y=3x+4 y=3x+3

Select the correct answer from the drop-down menu.

Answer 1

To determine the nature of the system of equations given by:

1. \( y = 3x + 4 \)
2. \( y = 3x + 3 \)

we can analyze the two equations. Both equations are in the slope-intercept form \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept.

- The slope of the first equation (\( y = 3x + 4 \)) is 3.
- The slope of the second equation (\( y = 3x + 3 \)) is also 3.

Since both equations have the same slope (3), they are parallel lines. However, their y-intercepts are different (4 and 3), which means that the lines will never intersect.

Since the lines do not intersect, this system of equations is inconsistent.

Thus, the correct option is: **inconsistent**.