Chapter 1.5, Problem 2E

Solution

To find: The $\left(x,y\right)$ pair for the value of the parameter.

The required value of $\left(x,y\right)$ pair is $\left(-17,23\right)$ .

Given data: The parametric values of x and y are $x=5t-7$ , $y=17-3t$ and $t=-2$ .

Method/Formula used:

Substitute value of t in the expressions for x and y .

Calculation:

The parametric values of x and y are $x=5t-7$ , $y=17-3t$ and $t=-2$ .

The coordinate pair $\left(x,y\right)$ is equivalent to pair $\left(x=5t-7,y=17-3t\right)$ can be written as,

  $\left(x,y\right)\equiv \left(5t-7,17-3t\right)$ … (1)

Substitute $-2$ for $t$ on the right of result (1),

  $\begin{array}{c}\left(x,y\right)\equiv \left(5t-7,17-3t\right)\\ \equiv \left(5\cdot (-2)-7,17-3\cdot (-2)\right)\\ \equiv \left(-10-7,17+6\right)\\ \equiv \left(-17,23\right)\end{array}$

Thus, the $\left(x,y\right)$ pair for parameter value $t=-2$ is $\left(-17,23\right)$.