Elimination Method to Solve 2x-3y=10 and 4x-6y=20:

To solve the given system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations. Here are the steps to follow:

Step 1: Multiply the first equation by 2 to make the coefficient of x the same as the second equation:
2x - 3y = 10 (multiply by 2)
4x - 6y = 20

The new system of equations is:
4x - 6y = 20
4x - 6y = 20

Step 2: Subtract one equation from the other to eliminate y:
4x - 6y = 20
- (4x - 6y = 20)
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0x + 0y = 0

This equation means that 0 = 0, which is always true. It tells us that the two equations are equivalent and have the same solution.

Step 3: Since y can have any value, we can choose any value for y and solve for x. Let's choose y = 0:
2x - 3(0) = 10
2x = 10
x = 5

Step 4: Now, we have found one solution (x = 5, y = 0). To find the general solution, we can use the equation we obtained in Step 2:
0x + 0y = 0

This equation tells us that y can have any value, so we can write the solution as:
x = 5, y = t (where t is any real number)

Therefore, the solution to the system of equations 2x-3y=10 and 4x-6y=20 is x = 5 and y = t, where t is any real number.

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