Answer
The system has infinitely many solutions, represented by-
$(x, \frac{1}{3} x - \frac{4}{3})$
where $x$ is any real number.
Work Step by Step
Given system is-
$25x -75y$ = $100$ __ eq.1
$-10x +30y$ = $-40$ __ eq.2
Multiplying eq.1 by 4 and eq.2 by -10
$100x -300y$ = $400$ __ eq.3
$100x -300y$ = $400$ __ 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-
$300y$ = $100 x - 400$
i.e. $y = \frac{100}{300} x - \frac{400}{300} $
i.e. $y = \frac{1}{3} x - \frac{4}{3} $
i.e. for every real value of $x$,
$y = \frac{1}{3} x - \frac{4}{3}$
Thus $(x, \frac{1}{3} x - \frac{4}{3})$ represent the solutions of given system.