Answer
The system has infinitely many solutions, represented by-
$(x, 3 - \frac{3}{2} x)$
where $x$ is any real number.
Work Step by Step
Given system is-
$6x +4y$ = $12$ __ eq.1
$9x +6y$ = $18$ __ eq.2
Multiplying eq.1 by 3 and eq.2 by 2
$18x +12y$ = $36$ __ eq.3
$18x +12y$ = $36$ __ 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-
$y = \frac{36}{12} - \frac{18}{12} x$
i.e. $y = 3 - \frac{3}{2} x$
i.e. for every real value of $x$,
$y = 3 - \frac{3}{2} x$
Thus $(x, 3 - \frac{3}{2} x)$ represent the solutions of given system.