Question

find integers s and t such that 1= 7*s + 11*t. Show that s and t are not unique

Answer 1

hint: 22 - 21 = 1

Answer 2

so s= -3 and t=2......but if they aren't unique I should show two other numbers that will work in this situation?

Answer 3

yes good, s = -3 and t = 2 is one solution

Answer 4

what's another solution? you only need one more to show that it's not unique

Answer 5

what about s= 8...and t= -5....then it's 56-55=1? and that's my answer?

Answer 6

good, that's another solution

Answer 7

thank you!!

Answer 8

there are infinitely many of these because they all lie on the line which is infinitely long

Answer 9

you're welcome

Answer 10

btw I'm sure you noticed this, but I might as well point it out (for anyone who isn't seeing it)

Answer 11

but you have s = -3 and t = 2

then you jumped to s = 8 and t = -5

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once you have s = -3 and t = 2, you can add 11 to -3 to get -3+11 = 8
the 11 comes from the coefficient of t

to counterbalance things, you subtract 7 from the value of t = 2 to get 2 - 7 = -5

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so that explains how you went from

s = -3 and t = 2

to

s = 8 and t = -5


to get another solution, add 11 to 8 to get 11+8 = 19 and subtract 7 from -5 to get -5 - 7 = -12

this means another solution is

s = 19 and t = -12

and this process can be repeated forever