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

Jul 3, 2016

$x = \frac{214}{435} \text{ and } y = - \frac{143}{435}$

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 $x = \ldots$ and then equate the two expressions obtained.

$11 x - 17 y = 11 \text{ and } - 59 x - 67 y = - 7$

$x = \frac{17 y + 11}{11} \text{ } \frac{7 - 67 y}{59} = x$

Now, using the fact that $\text{ "x = x " }$

It means that $\text{ "(17y +11)/11" } = \frac{7 - 67 y}{59}$

Cross multiply to get: $\left(17 \times 59\right) y + 11 \times 59 = 77 - \left(11 \times 67\right) y$

$1003 y + 737 y = 77 - 649$

$1740 y = - 572$
$y = - \frac{572}{1740} = - \frac{143}{435}$

$x = \frac{214}{435}$