How do I do simultaneous equations?

example: solve the simultaneous equations 3x+2y=4 and 2x+y=3

1:   3x+2y=4
2:   2x+y=3

want to either get same number of x's or same number of y's in equation 1 and equation 2
easiest way to do this is by making both equations contain 2y by multiplying equation 2 by 2

2x2: 2(2x+y=3)
        4x+2y=6   call this equation 3

now you have the same number of y's in both equations you can subtract one from the other so that there are no y's in the overall equation
choose the equation with the highest number of x's to subtract from so that you will not have a negative number of x's left over

3-1: (4x+2y)-(3x+2y)=6-4
       4x+2y-3x-2y=6-4
       4x-3x + 2y-2y = 6-4
       x+0=2
       therefore x=2

now you have found what x equals you can substitute this value back into one of your original equations (equation 1 or equation 2) to find the value of y. I will sub into 2 as there is only one y in the equation so less working out is needed

sub x into 2: 2x+y=3
                   2(2)+y=3
                   4+y=3
                   y=3-4
                   y=-1