That's not a linear system, but you have an awesome school system for giving you this problem.
Multiply by 6xy to clear the fractions.
That's a second degree equation, also known as a conic. That one happens to be a hyperbola.
Let's clear the fractions from the second equation, multiplying out common denominator xy:
We are being asked to find the meet of two hyperbolas, so we expect two answers, a quadratic equation.
Substituting,
We have to rule out x=0 because it's in the denominator.
Answer: (44/19, 33/20)