If you do not have equal equation coefficient for both variables can you still use the elimination method? how will you eliminate that variable

Yes, you just times one of the equations by a numberr to make it cancel out with the other. For instance:

2x + 6 y = 10
4x + 2y = 16

If we multiply the equation 2x + 6 y = 10 by 2 we get the following

2x + 6 y = 10
-2(2x + 6 y) = -2(10)
-4x -12y = -20
Now we use this new equation.
-4x -12y = -20
4x + 2y = 16

As you can see, you can cancel out the x and solve for y now.