How do you solve the following system?: #11x -17y =11, -59x -67y = -7#

Question

1394 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-03T17:15:24

#x = 214/435" and "y = -143/435#

Seriously??? This question is just ugly! All the numbers are primes numbers so the products are big and cumbersome..

However, it is of some comfort that even in a case like this, a method can be used to find an answer.

To keep the numbers as small as possible, let's change them both into #x = ...# and then equate the two expressions obtained.

#11x - 17y = 11 " and " -59x - 67y = -7#

#x = (17y +11)/11 " " (7 -67y)/59 = x#

Now, using the fact that # " "x = x " "#

It means that # " "(17y +11)/11" " = (7 -67y)/59 #

Cross multiply to get: #(17xx59)y + 11xx59 = 77 - (11xx67)y#

#1003y +737y = 77-649#

#1740y = -572#
#y = -572/1740 = -143/435#

#x = 214/435#