Answer
$(5, 21)$
Work Step by Step
Given system is-
$\frac{3}{2}x -\frac{1}{3}y$ = $\frac{1}{2}$ __ eq.1
$2x -\frac{1}{2}y$ = $-\frac{1}{2}$ __ eq.2
Multiplying eq.1 by 6 and eq.2 by 2
$9x -2y$ = $3$ __ eq.3
$4x -y$ = $-1$
i.e. $y$ = $4x+1$ __ eq.4
Substituting for $y$ in eq.3 from eq.4-
$9x -2(4x+1)$ = $3$
i.e. $9x -8x-2$ = $3$
i.e. $x$ = $3+2$ = $5$
Substituting for $x$ in eq.4
$y$ = $4(5)+1$
$y$ = $20+1$ = $21$
Thus $(5, 21)$ is the solution of given system.
