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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?

user130306
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1 Answers1

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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

  • thank you! sorry for a dumb question, but I'm still failing to see where you are adding this combination of $1069160-2294240$. I understand how that equals zero but are you adding it to $625(9160)-1350(4240)=1000$? I keep trying to add the LCM to that equation but I don't see how you are getting $2109$ and $-4556$. Sorry, I'm a bit slow. – user130306 May 19 '19 at 19:04
  • keep adding or subtracting the 0 part you'll eventually hit these values.You subtract the 0 part by changing x and y by the coefficients of the number they are linked to. –  May 19 '19 at 19:17
  • so basically i need to keep adding 106 to 625 until i get a value above 2018? – user130306 May 19 '19 at 20:14
  • and subtracting 229 the same amount off -1350. for the second reverse the operations. –  May 19 '19 at 23:20