Answer
$x=2, y=.5$
Work Step by Step
$\frac{2}{x}-\frac{3}{y} =-5$
$\frac{4}{x}+\frac{6}{y} =14$
$xy*(\frac{2}{x}-\frac{3}{y}) =xy*-5$
$xy*(\frac{4}{x}=\frac{6}{y}) =xy*14$
$2y-3x=-5xy$
$4y+6x=14xy$
$2*(2y-3x=-5xy)$
$4y+6x=14xy$
$4y-6x=-10xy$
$4y+6x=14xy$
$4y-6x+4y+6x=-10xy+14xy$
$8y=4xy$
$8y/4y=4xy/4y$
$2 = x$
$\frac{2}{x}-\frac{3}{y} =-5$
$\frac{2}{2}-\frac{3}{y} =-5$
$1-\frac{3}{y} =-5$
$1-\frac{3}{y}+5+\frac{3}{y} =-5+5+\frac{3}{y}$
$6 = 3/y$
$6*y/6=3/y*y/6$
$y=1/2$
