document.write( "Question 152193: Find two numbers whose sum is 23 and the difference of whose squares is 207 \n" ); document.write( "
Algebra.Com's Answer #111858 by mducky2(62)\"\" \"About 
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Any problem which has two variables can only be solved if there are at least two equations.
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Two numbers whose sum is 23:
\n" ); document.write( "x + y = 23
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The difference of whose squares is 207: (Let's make x represent the larger of the two):
\n" ); document.write( "x2 - y2 = 207
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Let's solve the first equation for x:
\n" ); document.write( "x + y = 23
\n" ); document.write( "x = 23 - y
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Now we can plug it into the second equation:
\n" ); document.write( "x2 - y2 = 207
\n" ); document.write( "(23-y)2 - y2 = 207
\n" ); document.write( "232 - 46y + y2 - y2 = 207
\n" ); document.write( "529 - 46y = 207
\n" ); document.write( "529 - 207 - 46y = 207 - 207
\n" ); document.write( "322 - 46 y = 0
\n" ); document.write( "322 = 46y
\n" ); document.write( "322/46 = 46y/46
\n" ); document.write( "y = 7
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Plugging into the first equation:
\n" ); document.write( "x = 23 - y
\n" ); document.write( "x = 16
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Therefore, y = 7 and x = 16\r
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