A graphical solution can be quick and easy. It shows the solution to be ...
(x, y) = (-1, 9)
__
Another suitable method is Cramer's rule. It makes use of a particular pattern of sum of products of coefficients and constants. The denominator in each case is the same sum of products.
x = (5(-29)-(-3)(31))/(5(2)-(-3)(14)) = -52/52 = -1