document.write( "Question 1188743: The sum of two numbers is 33. The sum of the squares of these numbers is 557. Find the two numbers. \n" ); document.write( "

Algebra.Com's Answer #819906 by VFBundy(438) $\"\"$ $\"About$

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Make two equations:
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\n" ); document.write( "x + y = 33
\n" ); document.write( "x² + y² = 557
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\n" ); document.write( "From the first equation, let: y = 33 - x
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\n" ); document.write( "Substitute y = 33 - x into the second equation:
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\n" ); document.write( "x² + (33 - x)² = 557
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\n" ); document.write( "Simplify and solve for x:
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\n" ); document.write( "x² + (1089 - 66x + x²) = 557
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\n" ); document.write( "2x² - 66x + 1089 = 557
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\n" ); document.write( "2x² - 66x + 532 = 0
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\n" ); document.write( "x² - 33x + 266 = 0
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\n" ); document.write( "(x - 14)(x - 19) = 0
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\n" ); document.write( "x = 14; x = 19
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\n" ); document.write( "There are two solutions. If you let x = 14 and substitute this into the original first equation (x + y = 33), this means y = 19.
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\n" ); document.write( "And, if you let x = 19 and substitute this into the original first equation (x + y = 33), this means y = 14.
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\n" ); document.write( "Either way, the two numbers you are looking for are 14 and 19. \n" ); document.write( "

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