Answer
$\frac{16}{7}, -\frac{14}{3})$
Work Step by Step
Given the system of equations:
1. $3x + \frac{4}{y} = 6$
2. $x - \frac{8}{y} = 4$
It asks to find all solutions.
Multiply equation 1 by 2, then add the result to equation 2
$6x + \frac{8}{y} = 12$
+ ($x - \frac{8}{y} = 4$)
$7x = 16$
$x = 16/7$
$3 (16/7) + \frac{4}{y} = 6$
$48/7 + \frac{4}{y} = 6$
$\frac{4}{y} = -6/7$
$\frac{-14}{3} = y$
Thus the solution is $\frac{16}{7}, -\frac{14}{3})$
See graph below.
The red line is graph 1; the blue line is graph 2
