Eliminating Parameter to find Cartesian equations

Question

When eliminating the parameter to find a Cartesian equation of the curve below when do we know when the Cartesian equation is solved for x and when it’s solved for y?

x=3t+2

y=2t+3

Answer 1

x = 3t + 2 and y = 2t + 3

Since x = 3t + 2, t = (x - 2) /3

So, y = 2[(x-2) / 3] + 3

y = (2/3)x + (5/3)

This is a line with slope 2/3 and y-intercept (0, 5/3).