Solve the system below with the elimination method. Submit your answer as an ordered pair (x,y) without spaces. If there is more than one solution, enter (x,mx-b) where m and b are integers. If there is no solution, write: No Solution

6x - 10y = 3

1.5x - 2.5y = -0.75

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.

Learn how to solve systems of equations using the elimination method with a detailed step-by-step solution for the equations 6x - 10y = 3 and 1.5x - 2.5y = -0.75. This problem demonstrates the application of the elimination method in solving linear equations. Suitable for students in Grades 9-12.

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