Answer
The system has infinitely many solutions, represented by-
$(x, \frac{1}{3} x - \frac{5}{3})$
where $x$ is any real number.
Work Step by Step
Given system is-
$2x -6y$ = $10$ __ eq.1
$-3x +9y$ = $-15$ __ eq.2
Multiplying eq.1 by 3 and eq.2 by -2
$6x -18y$ = $30$ __ eq.3
$6x -18y$ = $30$ __ 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-
$y = \frac{6}{18} x - \frac{30}{18}$
i.e. $y = \frac{1}{3} x - \frac{5}{3}$
i.e. for every real value of $x$,
$y = \frac{1}{3} x - \frac{5}{3}$
Thus $(x, \frac{1}{3} x - \frac{5}{3})$ represent the solutions of given system.
