Question 1079503

 

A  parametric equation in a plane consists of two equations 
{{{x = f(t)}}} and {{{y = g( t )}}} where {{{x }}}and {{{y}}} are ordered pairs and {{{t}}} is the parameter.

Given: 
{{{x = 2/(10 - t)}}} 
{{{ y = (2t + 1)}}}, eliminate the parameter. 

First solve the equation {{{x =2/(10 - t)}}}  for the parameter, {{{t}}}:

{{{x(10 - t)  =2}}}

{{{10x -x* t  =2}}}

{{{10x -2 =x* t}}}
 
{{{10x/x -2/x = t }}}

{{{t=10 -2/x}}}


Then substitute the expression into the other parametric equation for {{{t}}}:

{{{ y = (2t + 1)}}}

 {{{y = 2(10 -2/x)+ 1}}}

 {{{ y = 20 -4/x+ 1}}}

 {{{ y = 21 -4/x}}}

so, your answer is: D.) {{{ y = 21 - 4/x }}}