#### Answer

Infinitely many solutions.

#### Work Step by Step

Eq. 1: $\frac{1}{2}x - \frac{1}{3}y$ = 1
Eq. 2: $-2x + \frac{4}{3}y$ = -4
If we multiply equation 1 by -4, the equation will become:
-4($\frac{1}{2}x - \frac{1}{3}y$) = -4(1)
$\frac{-4}{2}x - \frac{-4}{3}y$ = -4
$-2x + \frac{4}{3}y$ = -4
Equations 1 and 2 are the same. Their graphs will coincide, meaning that all points on one line overlay all points on the other, so every point will be a solution. Plugging values in for both equations will return the same answer for every point in both equations. Therefore, there are infinitely many solutions.