Easy formula thats giving me problems Im getting that the GC

Easy formula that\'s giving me problems..

I\'m getting that the GCD is 5, but when I try to solve the formula I get no real answer, and I\'m stuck on what to put on my homework.

Idk, if i\'m doing it wrong, so that\'s why I\'m asking. When I try to solve the equation I get 5-70y+70y=5

Find a pair of integers T and y such that 5r+ 70y gcd(55, 70) (x,y)-1/11(1

Solution

55 = 5*11 and 70 = 2* 5*7 . Therefore gcd( 55,70) = 5.

Then 55x + 70 y = 5 or, 11x + 14y = 1. Obviously, both x and y can not be postive or both negative. One of x and y is positive and the other negative. Let x be negative and y be positive. Since 11x + 14y = 1, therefore x = 1/11 ( 1 - 14y) . Then 1 - 14y has to be a multiple of 11. The least value of y for which 1-14y is a multiple of 11 is 4. When y = 4, we have 1 - 14 y = 1 - 14 * 4 = 1 - 56 = - 55 . Then x 1/11 ( 1 - 14y) = 1/11( -55) = -5. Thus, one of the answers is ( x , y) = ( - 5, 4 )