## Rewrite the parametric equation by eliminating the parameter x=4t+1 and y=t-3

Question

Rewrite the parametric equation by eliminating the parameter x=4t+1 and y=t-3

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6 days 2021-10-11T19:23:24+00:00 1 Answer 0

The equation is x = 4y + 13

Step-by-step explanation:

* Lets talk about the parametric equations

– Parametric equations are a set of equations that express a set

of quantities as explicit functions of a number of independent

variables

– Ex: x = at + b and y = ct + d are parametric equations

– We use them to find relation between the variables x and y

* Lets solve the problem

∵ x = 4t + 1 ⇒ (1)

∵ y = t – 3 ⇒ (2)

– The parameter is t to eliminate it find t in terms of x or y

– We will use equation (2) to find t in terms of y

∵ y = t – 3 ⇒ add 3 to both sides

∴ t = y + 3 ⇒ (3)

– Substitute the value of t in equation (3) in equation (1)

∵ x = 4t + 1

∵ t = y + 3

∴ x = 4(y + 3) + 1 ⇒ open the bracket

∴ x = 4y + 12 + 1 ⇒ add like term

∴ x = 4y + 13

* The equation is x = 4y + 13