Answer
$(10, -9)$
Work Step by Step
Given system is-
$\frac{1}{2}x +\frac{1}{3}y$ = $2$ __ eq.1
$\frac{1}{5}x -\frac{2}{3}y$ = $8$ __ eq.2
Multiplying eq.1 by 'LCM' of 2 and 3 i.e. '6'-
$3x +2y$ = $12$ __ eq.3
Multiplying eq.2 by 'LCM' of 5 and 3 i.e. '15'-
$3x -10y$ = $120$ __ eq.4
Subtracting eq.3 from eq.4-
$ (3x -10y)-(3x +2y)$ = $120-12$
i.e. $ 3x -10y-3x -2y$ = $108$
i.e. $ -12y$ = $108$
i.e. $ y$ = $\frac{108}{-12}$ = $-9$
Substituting for y in eq.3-
$3x +2(-9)$ = $12$
i.e. $3x -18$ = $12$
i.e. $3x $ = $12+18$= $30$
i.e. $x $ = $10$
Thus $(10, -9)$ is the solution of given system.