Problem: The number of solutions of 22x−32y=55, in which x and y are integers, is:
Answer Choices:
A. Zero
B. One
C. Two
D. Three
E. More than three, but finite
Solution:
2xx−3xy∴2x+3y2x−3y2⋅2xxy=(2x+3y)(2x−3y)=11⋅5=55⋅1=11=5=16=3=12x+3y=552x−3y=1This system does not yieldintegral values for x and y