solve using any appropriate method
10x+y=278
10y+x=107
I chose wolframalpha.com, which you can always use to verify your solutions.
http://www.wolframalpha.com/input/?i=solve+10x%2By%3D278%2C+10y%2Bx%3D107+
10x+y=278
10y+x=107
http://www.wolframalpha.com/input/?i=solve+10x%2By%3D278%2C+10y%2Bx%3D107+