document.write( "Question 868572: Find the points of intersection of the line 3x+2y=10, with the curve x^2-xy+y^2=21 \n" ); document.write( "

Algebra.Com's Answer #523642 by Fombitz(32388) $\"\"$ $\"About$

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$\"3x%2B2y=10\"$
\n" ); document.write( " $\"2y=10-3x\"$
\n" ); document.write( " $\"y=5-%283%2F2%29x\"$
\n" ); document.write( "Substitute,
\n" ); document.write( " $\"x%5E2-xy%2By%5E2=21\"$
\n" ); document.write( " $\"x%5E2-x%285-%283%2F2%29x%29%2B%285-%283%2F2%29x%29%5E2=21\"$
\n" ); document.write( " $\"x%5E2-5x%2B%283%2F2%29x%5E2%2B%2825-15x%2B%289%2F4%29x%5E2%29=21\"$
\n" ); document.write( " $\"%2819%2F4%29x%5E2-20x%2B25=21\"$
\n" ); document.write( " $\"%2819%2F4%29x%5E2-20x%2B4=0\"$
\n" ); document.write( " $\"19x%5E2-80x%2B16=0\"$
\n" ); document.write( " $\"%28x-4%29%2819x-4%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"x-4=0\"$
\n" ); document.write( " $\"x=4\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"y=5-%283%2F2%294\"$
\n" ); document.write( " $\"y=5-6\"$
\n" ); document.write( " $\"y=-1\"$
\n" ); document.write( "and
\n" ); document.write( " $\"19x-4=0\"$
\n" ); document.write( " $\"19x=4\"$
\n" ); document.write( " $\"x=4%2F19\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"y=5-%283%2F2%29%284%2F19%29\"$
\n" ); document.write( " $\"y=5-6%2F19\"$
\n" ); document.write( " $\"y=89%2F19\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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