Convert these two parametric equations into one rectangular equation?

Question

x(t) = (5t^2)+(5/3)t-3

y(t) = (3t^2)+t+3

 

find y=f(x)

Answer 1

x(t) = 5t² + (5/3)t - 3

 

y(t) = 3t² + t + 3

 

Multiply the first equation by -3/5:

 

     (-3/5)x(t) = -3t² - t + 9/5

 

             y(t) = 3t² + t + 3

 

Add the equations to get:  (-3/5)x(t) + y(t) = 24/5

 

                                 So,  (-3/5)x + y = 24/5

 

                      y = (3/5)x + (24/5) = f(x)