Question 110684
Yes there is!

Your starting work is immpecable!
{{{x+y = 44}}}
{{{x-y = 22}}} Now just add these two equations:
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{{{2x = 66}}} so...
{{{x = 33}}}
Now for y...
{{{x-y = 22}}}
{{{33-y = 22}}}
{{{y = 11}}}