Describe the system 6x-2y=10 and 9x-3y=8 as consistent and independent, consistent and dependent, or inconsistent. Explain.

Answer:
When you multiply the second equation by 2/3, both equations become equal. Therefore there are many solutions. The system is consistent and dependent.

To determine whether the system of equations is consistent and independent, consistent and dependent, or inconsistent, we need to analyze the relationship between the two equations.

Let's rearrange the given equations in standard form:

Equation 1: 6x - 2y = 10 ...........(1)
Equation 2: 9x - 3y = 8 ...........(2)

We can see that equation 2 is obtained by multiplying equation 1 by 3/2:

By multiplying equation 1 by 3/2, we get: 9x - 3y = 15

Comparing equation 2: 9x - 3y = 8
with equation 9x - 3y = 15

We can see that both equations have the same left-hand side (9x - 3y), but different right-hand sides (8 and 15). This implies that the equations do not represent the same line, but instead, they are parallel lines.

Since the lines are parallel and never intersect, there are no common solutions for the two equations. Therefore, the system is inconsistent.

Therefore, the correct assessment of the system 6x - 2y = 10 and 9x - 3y = 8 is "inconsistent."