you have given one equation and there are two variables x and y.
2(x-1) + 3(y-2) = 1 or 2 x + 3y = 9
or x/4.5 + y /3 = 1 or y = 3 - 2/3 x
It is a straight line on the graph with x intercept as 4.5 units and y intercept being 3 units.
rewrite it as : y = 3 - 2/3 x
there are infinite number of solutions, if x ∈ (-∞, ∞).
As for each real value of x , there is a real value of y , as above.
Solutions are in the form of couples: or coordinates: (x , 3 - 2 x / 3 ), x∈ R