document.write( "Question 1088550: Eliminate the parameter in the equation x=3-2t, y=2+3t to find the corresponding rectangular equation. \n" ); document.write( "

Algebra.Com's Answer #702831 by MathLover1(20849) $\"\"$ $\"About$

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Eliminate the parameter in the equation $\"x=3-2t\"$ , \r
\n" ); document.write( "\n" ); document.write( " $\"y=2%2B3t\"$ to find the corresponding rectangular equation\r
\n" ); document.write( "\n" ); document.write( "The variable $\"t+\"$ in the parametized equations is \"the same\" $\"t\"$ : Both $\"x+\"$ and $\"y+\"$ are defined in terms of the same variable $\"t\"$ .\r
\n" ); document.write( "\n" ); document.write( "So in solving for $\"t\"$ in terms of $\"y\"$ , we have:
\n" ); document.write( " $\"y-2=3t\"$
\n" ); document.write( " $\"t=y%2F3-2%2F3\"$ , we can use this \"definition\" of $\"t+\"$ by substituting it into the equation for $\"x\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"x=3-2t\"$ .......substitute $\"t+\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x=3-2%28y%2F3-2%2F3%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=3-2y%2F3%2B4%2F3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x=+-2y%2F3%2B3%2B4%2F3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x=+-%282%2F3%29y%2B13%2F3\"$ ...this gives us function $\"x%28y%29\"$ which is a line\r
\n" ); document.write( "\n" ); document.write( "or, in standard form: $\"3x%2B2y=13\"$ \r
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