document.write( "Question 163815: The sum of two integers is fifteen. Eight times the smaller is 1 less than three times the larger. Find the numbers. \n" ); document.write( "
Algebra.Com's Answer #120682 by nerdybill(7384)\"\" \"About 
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I'll use the \"elmination method\"...
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\n" ); document.write( "Let x = smaller number
\n" ); document.write( "and
\n" ); document.write( "y = larger number
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\n" ); document.write( "Since we have two unknowns, we'll need to find two equations.
\n" ); document.write( "Equation 1 can be extracted from \"The sum of two integers is fifteen\":
\n" ); document.write( "x + y = 15
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\n" ); document.write( "Equation 2 can be extracted from \"Eight times the smaller is 1 less than three times the larger.\":
\n" ); document.write( "8x = 3y -1
\n" ); document.write( "rearranging:
\n" ); document.write( "8x - 3y = -1
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\n" ); document.write( "The two equations now are:
\n" ); document.write( "x + y = 15
\n" ); document.write( "8x - 3y = -1
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\n" ); document.write( "Multiplying the top equation by 3 to get:
\n" ); document.write( "3x + 3y = 45
\n" ); document.write( "8x - 3y = -1
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\n" ); document.write( "Adding the two equations together:
\n" ); document.write( "3x + 3y = 45
\n" ); document.write( "8x - 3y = -1
\n" ); document.write( "-------------
\n" ); document.write( "11x = 44
\n" ); document.write( "dividing both sides by 11:
\n" ); document.write( "x = 4 (smaller number)
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\n" ); document.write( "larger number is found by substituting the above into equation 1:
\n" ); document.write( "x + y = 15
\n" ); document.write( "4 + y = 15
\n" ); document.write( "y = 11 (larger number)
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\n" ); document.write( "Ans: 4 and 11 \n" ); document.write( "
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