Question 759534
Could the two equations be arranged so that a value for r makes them equivalent equations?


{1}   x-ry=r

{2}  x-(r-2)y=2
x-ry+2y=2


But no matter:  you still want the system in some consistant form.
{1}  x-ry=r
{2}  x-(r-2)y=2
How could these two equations be identical?
You would need r-2=r and r=2.  The one says, r=2 and the other says -2=0 which is nonsense.


Try putting both into slope-intercept form:
{1} {{{-ry=-x+r}}}, {{{y=(1/r)x-1}}}
{2} {{{-ry+2y=-x+2}}}, {{{y(2-r)=-x+2}}}, {{{y=-(1/(2-r))x+2/(2-r)}}}, {{{y=(1/(r-2))x+2/(2-r)}}}

The slopes will need to be equal if you want NO solution.
Must have:  {{{(1/r)=(1/(r-2))}}}
Meaning, you must have {{{r=r-2}}}.  This is impossible.  At least, impossible if only two dimensions, which is an assumption here.