Question 108460
Your wording is a bit confusing,
"show that -(x-y) is equal to x-y"
this cannot be unless both x and y are zero.
I think you mean  
"show that -(x-y) is equal to y-x"
{{{-(x-y)=y-x}}}
{{{-x-(-y)=y-x}}} Distributive property
{{{-x+y=y-x}}}Negative times negative equals a positive.
{{{y-x=y-x}}}
Since you deduced a true statement, your original equation is correct.
Therefore
{{{-(x-y)=y-x}}}