Eliminate the parameter for the following set of parametric equations show your work

X = t + 6
Y = 3t - 1

x = t + 6

Subract 6 to both sides

x - 6 = t

t = x - 6

y = 3 t - 1

y = 3 ( x - 6 ) - 1

y = 3 x - 18 - 1

y = 3 x - 19

To eliminate the parameter, t, we need to express one variable, either x or y, solely in terms of the other variable. Let's do that step by step:

1. Start with the given parametric equations:

X = t + 6
Y = 3t - 1

2. Solve the first equation, X = t + 6, for t:

X - 6 = t

3. Substitute this expression for t into the second equation, Y = 3t - 1:

Y = 3(X - 6) - 1

4. Simplify the equation:

Y = 3X - 18 - 1
= 3X - 19

Therefore, by eliminating the parameter t, we obtain the equation Y = 3X - 19, which relates x and y without the need for the parameter.