Question 1088550
Eliminate the parameter in the equation {{{x=3-2t}}}, 

{{{y=2+3t}}} to find the corresponding rectangular equation

The variable {{{t }}} in the parametized equations is "the same" {{{t}}}: Both {{{x }}}and {{{y }}} are defined in terms of the same variable {{{t}}}.

So in solving for {{{t}}} in terms of {{{y}}}, we have: 
{{{y-2=3t}}} 
{{{t=y/3-2/3}}} , we can use this "definition" of {{{t }}}by substituting it into the equation for {{{x}}}:


{{{x=3-2t}}}.......substitute {{{t }}}


{{{x=3-2(y/3-2/3)}}}

{{{x=3-2y/3+4/3}}}


{{{x= -2y/3+3+4/3}}}


{{{x= -(2/3)y+13/3}}}...this gives us function {{{x(y)}}} which is a line

or, in standard form:  {{{3x+2y=13}}}