What are the possible values of x and y when 29x plus 23y equals 23.29 showing work in detail?

In this type of problem let the numerator of a fraction be 23.29 and its denominator be twice the coefficient of the variables and so:-

29*(23.29/58)+23*(23.29/46) = 23.29

Therefore the possible values of x and y are 23.29/58 and 23.29/46 respectively