document.write( "Question 825720: What are the two numbers
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Algebra.Com's Answer #497546 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "What are the two numbers whose sum is 23 and its absolute difference is 5?\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "Let x be the first number.\r\n" );
document.write( "Let y be the second number.\r\n" );
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document.write( "The sum of two numbers is 23, so\r\n" );
document.write( "x + y = 23\r\n" );
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document.write( "The absolute difference between the numbers is 5, so\r\n" );
document.write( "|x - y| = 5\r\n" );
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document.write( "Now solve this system of equations using substitution.\r\n" );
document.write( "Rewrite the first equation in \"x=\" form.\r\n" );
document.write( "x = 23 - y\r\n" );
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document.write( "Substitute 23-y for win the second equation.\r\n" );
document.write( "|x - y| = 5\r\n" );
document.write( "|(23 - y) - y| = 5\r\n" );
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document.write( "Simplify.\r\n" );
document.write( "|23 - 2y| = 5\r\n" );
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document.write( "Then, either 23 - 2y = 5 OR -(23 - 2y) = 5. Solve both sides of the inequality for y.\r\n" );
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document.write( "23 - 2y = 5\r\n" );
document.write( "-2y = 5 - 23\r\n" );
document.write( "-2y = 18\r\n" );
document.write( "y = -9\r\n" );
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document.write( "OR\r\n" );
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document.write( "-(23-2y) = 5\r\n" );
document.write( "-23 + 2y = 5\r\n" );
document.write( "2y = 28\r\n" );
document.write( "y = 14.\r\n" );
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document.write( "If y = -9, then x + (-9) = 23 and x = 34 because the sum of the numbers is 23. However \r\n" );
document.write( "the absolute difference between -9 and 34 is 43 because |34 - (-9)| = 43. The pair, -9 and \r\n" );
document.write( "34, is not a solution.\r\n" );
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document.write( "If y = 14, then x + 14 = 23 and x = 9 because the sum of the numbers 23. We see that the \r\n" );
document.write( "absolute difference between 9 and 14 is 5 because |9 - 14| = 5.\r\n" );
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document.write( "The two numbers are 9 and 14.\r\n" );
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document.write( "Hope this helps!\r\n" );
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document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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