To solve the system of equations using the elimination method, we first rewrite both equations in a standard form:

1. $2x - 3y = 1$
2. $3 - 6x = -3$

Let's rearrange the second equation so that it is in the same form as the first:

$-6x = -3 - 3$

$-6x = -6$

Dividing both sides by -6:

$x = 1$

Now, substitute $x = 1$ back into the first equation:

$2(1) - 3y = 1$

Simplify:

$2 - 3y = 1$

Subtract 2 from both sides:

$-3y = -1$

Divide by -3:

$y = \frac{1}{3}$

Solution:

$x = 1, \quad y = \frac{1}{3}$

Would you like more details on any of these steps, or do you have any questions?

Related Questions:

1. How would you solve this system of equations using substitution?
2. How can you check the solution of a system of equations?
3. What are the advantages of using the elimination method?
4. How would you graphically represent the solution of this system of equations?
5. Can you explain how elimination differs from substitution in solving systems of equations?

Tip: When solving by elimination, always align the equations in a standard form and look for ways to eliminate one variable by addition or subtraction.