Is this the line you are talking about? There is a 35 in the left side so you get 3.35 on the right.5 = 35 – 2·(50 – 1·35) = 3·35 – 2·50
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This comes from my notes. At the bottom where it says: 2*(50 - 1*35) = 3*35 - 2*50,
I am not figuring out 3 and the 2 come from in 3*35 - 2*50. I tried multiplying which gives me the 2*50 but the 3*35 I do not understand how they getting that.
This is easier with an example:
Solve 135x + 50y = gcd(135, 50)
135 = 2·50 + 35
50 = 1·35 + 15
35 = 2·15 + 5
15 = 3·5 + 0, so gcd(135, 50) = 5
5 = 35 – 2·15
15 = 50 – 1·35,
so 5 = 35 – 2·(50 – 1·35) = 3·35 – 2·50
35 = 135 – 2·50,
so 5 = 3·(135 – 2·50) – 2·50 = 3·135 – 8·50 (x = 3, y = -8)
I just figured out how they got it.
This is what I see:
35 – 2·(50 – 1·35) = 3·35 – 2·50
35 - 2·(50) + 2·(35)
Clic-Clac, when you told me about the extra 35, I am looking at it like this:
1·(35) - 2·(50) + 2·(35)
Since (35) are common, we add them, giving me:
- 2·(50) + 3·(35)
Thats what I needed to figure out.
Thanks for your help Clic-Clac