How to find out where 2 lines cross/simultaneous equations

If we have the 2 lines

line 1 - 3y=4x+2 and line 2 - 6y=7x+3

Firstly we would look for when the y's or x's are multiples of each other in this case the y's are multiples of each other as 3 is a multiple of 6.

Therefore we would times line 1 by 2 to become 6y=8x+4 -line 3

we then use line 2 and 3 as simultaneous equations to try and only have one variable in this case x.

line 2 - line 3 will give us     0=-x-1, so rearranging and moving x to the other side of the equation x=-1, then we put this back into any of the 3 lines to find out what y equals at this point.

So using line 1.. 3y= 4(-1)+2 so 3y=-2 so y=-2/3

so the lines 1 and 2 intersect at the point (-1,-2/3)