Question 760423
Those equations are begging to get simplified and rearranged into an equivalent, simple, more standard form.
{{{-6x-4y=18}}} --> {{{6x+4y=-18}}} --> {{{3x+2y=-9}}} (multiplying both sides of the equal sign times (-1) and then dividing by 2 both sides of the equal sign )
{{{4y=-6x-18}}} --> {{{6x+4y=-18}}} --> Wait. I do not need to go further. Both equations are equivalent to {{{6x+4y=-18}}}.
They both represent the same line. There is an infinite number of (x,y) pairs that satisfy both equations:all the points on the line {{{6x+4y=-18}}}.
 
The equations in the next system represent lines that are not the same and are not parallel, so there is a unique (x,y) pair that is the solution of the system:
{{{2x+2y=2}}} --> {{{x+y=1}}} <--> {{{y=1-x}}} (a line with slope=-1)
{{{y=3-3x}}} (a line with slope=-3)
{{{system(2x+2y=2,y=3-3x)}}} --> {{{system(x+y=1,y=3-3x)}}} --> {{{system(y=1-x,y=3-3x)}}} --> {{{system(y=1-x,1-x=3-3x)}}} --> {{{system(y=1-x,1+2x=3)}}} -->  {{{system(y=1-x,2x=2)}}} --> {{{system(y=1-x,x=1)}}} --> {{{system(y=1-1,x=1)}}} --> {{{highlight(system(y=0,x=1))}}}