anonymous
  • anonymous
find integers s and t such that 1= 7*s + 11*t. Show that s and t are not unique
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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jim_thompson5910
  • jim_thompson5910
hint: 22 - 21 = 1
anonymous
  • anonymous
so s= -3 and t=2......but if they aren't unique I should show two other numbers that will work in this situation?
jim_thompson5910
  • jim_thompson5910
yes good, s = -3 and t = 2 is one solution

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jim_thompson5910
  • jim_thompson5910
what's another solution? you only need one more to show that it's not unique
anonymous
  • anonymous
what about s= 8...and t= -5....then it's 56-55=1? and that's my answer?
jim_thompson5910
  • jim_thompson5910
good, that's another solution
anonymous
  • anonymous
thank you!!
jim_thompson5910
  • jim_thompson5910
there are infinitely many of these because they all lie on the line which is infinitely long
jim_thompson5910
  • jim_thompson5910
you're welcome
jim_thompson5910
  • jim_thompson5910
btw I'm sure you noticed this, but I might as well point it out (for anyone who isn't seeing it)
jim_thompson5910
  • jim_thompson5910
but you have s = -3 and t = 2 then you jumped to s = 8 and t = -5 ------------------------------------------------------- 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 ------------------------------------------------------- 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

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