So I have $9160x+4240y=1000$ Using the EA to find the gcd, I get that it is equal to 40.
Solving for the RHS and working backwards, I have:
$$40=680-160*4$$
$$160=4240-680$$
$$680 = 9160-4240*2$$
Doing all the substitutions, I have $$40=25(9160)-54(4240)$$
So, $$625(9160)-1350(4240)=1000$$
How can I make it so that the x-coordinate is above 2018? that's the part I'm confused about because the x coordinate is 625, and then how do i calculate the y coordinate. also if I was asked to make the y-coordinate positive, how would I do that so that 1350 is no longer there and is now something positive?
The hint given, was add a form of 0. What that means is add 0 to both sides, one directly and one by figuring out the lcm of 9160 and 4240 is $$970960=106\cdot9160=229\cdot 4240$$ and then say:$$106\cdot9160-229\cdot 4240=0$$ so moving x up 106, needs y falling by 229 to cancel out. Likewise, x falling by 106 needs an increase of y by 229 to cancel out. These movements done in the given combinations, don't change the difference at hand. They add or subtract 0 the RHS in otherwords.
Solutions
x=2109,y=-4556
x=-11,y=24