document.write( "Question 371715: (4x^2)+(9y^2)=16
\n" ); document.write( "2x+3y=4 \n" ); document.write( "

Algebra.Com's Answer #264816 by Fombitz(32388) $\"\"$ $\"About$

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This is the intersection of a line with an ellipse.
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\n" ); document.write( "1. $\"%284x%5E2%29%2B%289y%5E2%29=16\"$
\n" ); document.write( "2. $\"2x%2B3y=4\"$
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\n" ); document.write( "From eq. 2,
\n" ); document.write( " $\"2x=4-3y\"$
\n" ); document.write( " $\"4x%5E2=%284-3y%29%5E2\"$
\n" ); document.write( " $\"4x%5E2=16-24y%2B9y%5E2\"$
\n" ); document.write( "Substitute into eq. 1,
\n" ); document.write( " $\"%2816-24y%2B9y%5E2%29%2B9y%5E2=16\"$
\n" ); document.write( " $\"18y%5E2-24y=0\"$
\n" ); document.write( " $\"6y%283y-4%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"6y=0\"$
\n" ); document.write( " $\"highlight%28y=0%29\"$
\n" ); document.write( "Then from eq. 2,
\n" ); document.write( " $\"2x%2B0=4\"$
\n" ); document.write( " $\"highlight%28x=2%29\"$
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\n" ); document.write( " $\"3y-4=0\"$
\n" ); document.write( " $\"3y=4\"$
\n" ); document.write( " $\"highlight_green%28y=4%2F3%29\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"2x%2B3%284%2F3%29=4\"$
\n" ); document.write( " $\"2x%2B4=4\"$
\n" ); document.write( " $\"2x=0\"$
\n" ); document.write( " $\"highlight_green%28x=0%29\"$
\n" ); document.write( "The two intersection points are ( $\"2\"$ , $\"0\"$ ) and ( $\"0\"$ , $\"4%2F3\"$ ).
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