Elimination Method to Solve for x and y:

To solve for x and y using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations. Here's how we can solve the given equations:

Step 1: Multiply the first equation by 2 to eliminate x and get:

4x - 6y = 20

Step 2: Now, we can subtract the second equation from the first equation to eliminate y and get:

(4x - 6y) - (4x - 6y) = 20 - 10

0 = 10

Step 3: The result is an inconsistent equation which means that there is no solution for x and y that satisfies both equations. Therefore, the given equations are inconsistent and do not have a unique solution.

Explanation:

The given equations are:

2x - 3y = 10 …(1)
4x - 6y = 20 …(2)

To solve for x and y, we need to eliminate one of the variables by adding or subtracting the equations. In this case, we can eliminate y by multiplying equation (1) by 2 to get:

4x - 6y = 20

Now, we can subtract equation (2) from equation (1) to eliminate y and get:

(4x - 6y) - (4x - 6y) = 20 - 10

0 = 10

The result is an inconsistent equation which means that there is no solution for x and y that satisfies both equations. Therefore, the given equations are inconsistent and do not have a unique solution.

Conclusion:

The elimination method is a useful technique to solve a system of linear equations. However, it might not always work, especially when the equations are inconsistent or dependent. In such cases, we need to use other methods such as substitution or graphical methods to solve the equations.