Question

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

Answer 1

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

Explanation:

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`