SOLUTION: For what value of r the equtions, x-ry=r and x-(r-2)y=2 do not have any solution.

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Question 759534: For what value of r the equtions, x-ry=r and
x-(r-2)y=2 do not have any solution.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Br, y=%281%2Fr%29x-1
{2} -ry%2B2y=-x%2B2, y%282-r%29=-x%2B2, y=-%281%2F%282-r%29%29x%2B2%2F%282-r%29, y=%281%2F%28r-2%29%29x%2B2%2F%282-r%29
The slopes will need to be equal if you want NO solution.
Must have: %281%2Fr%29=%281%2F%28r-2%29%29
Meaning, you must have r=r-2. This is impossible. At least, impossible if only two dimensions, which is an assumption here.