Answer:
The equation is x = 4y + 13
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