Answer
The system has infinitely many solutions, represented by-
$(x, 5 - \frac{5}{6} x )$
where $x$ is any real number.
Work Step by Step
Given system is-
$\frac{1}{2}x +\frac{3}{5}y$ = $3$ __ eq.1
$\frac{5}{3}x +2y$ = $10$ __ eq.2
Multiplying eq.1 by 10 and eq.2 by 3
$5x +6y$ = $30$ __ eq.3
$5x +6y$ = $30$ __ eq.4
We see that both the equations in the system represent the same line. The coordinates of any point on this line give a solution of the system. Thus the system has infinitely many solutions.
Writing the equation in slope-intercept form, we have-
$6y$ = $30 - 5x$
i.e. $y = \frac{30}{6} - \frac{5}{6}x $
i.e. $y = 5 - \frac{5}{6} x $
i.e. for every real value of $x$,
$y = 5 - \frac{5}{6} x $
Thus $(x, 5 - \frac{5}{6} x )$ represent the solutions of given system.