Question

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

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

Select the correct answer from the drop-down menu.


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Answer 1

To determine if the system of equations is consistent and independent, consistent and dependent, or inconsistent, we should first rearrange the equations:

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

Now, we can set the two equations equal to each other since they both equal \( y \):

\[
3x + 4 = 3x + 3
\]

Subtracting \( 3x \) from both sides:

\[
4 = 3
\]

This statement is false, indicating that the two lines represented by the equations are parallel and do not intersect. Therefore, the system of equations is inconsistent.

**Answer:** Inconsistent