To solve the given system of equations using the elimination method, we start by writing down the equations:

$6x - 10y = 3$ $1.5x - 2.5y = -0.75$

First, let's clear the decimal in the second equation by multiplying it by 4:

$4 \times (1.5x - 2.5y) = 4 \times (-0.75)$

This simplifies to:

$6x - 10y = -3$

Now, we have the system:

$6x - 10y = 3$ $6x - 10y = -3$

Next, we subtract the second equation from the first equation:

$(6x - 10y) - (6x - 10y) = 3 - (-3)$

This simplifies to:

$0 = 6$

Since this is a contradiction (0 does not equal 6), it means that there is no solution to the system of equations. Therefore, the system is inconsistent.

Thus, the answer is:

$\text{No Solution}$

Do you want details or have any questions? Here are some questions you might want to ask:

1. How do you solve systems of equations using the substitution method?
2. Can you explain the graphing method for solving systems of equations?
3. What are some real-life applications of solving systems of equations?
4. How do you determine if a system of equations has infinitely many solutions?
5. Can you solve a system of equations involving three variables?

Tip: Always check your final results by substituting back into the original equations to ensure accuracy.