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From the information in the problem we can write two equations. The first equation
\n" ); document.write( "comes from the fact that one number (call it x) and another number (call it y) add
\n" ); document.write( "up to be 66. So the first of our equations is:
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\n" ); document.write( "x + y = 66
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\n" ); document.write( "The second equation comes from the information that x is 3 more than twice y. In equation
\n" ); document.write( "form this can be written as:
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\n" ); document.write( "x = 2y + 3
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\n" ); document.write( "Substitute this into the first equation by replacing x by 2y + 3 and the first equation
\n" ); document.write( "becomes:
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\n" ); document.write( "2y + 3 + y = 66
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\n" ); document.write( "Subtract 3 from both sides for the purpose of eliminating the + 3 from the left side. When
\n" ); document.write( "you do this subtraction the equation becomes:
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\n" ); document.write( "2y + y = 63
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\n" ); document.write( "Add the terms on the left side and you get:
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\n" ); document.write( "3y = 63
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\n" ); document.write( "Divide both sides by 3 to find that:
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\n" ); document.write( "y = 63/3 = 21
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\n" ); document.write( "Since x + y = 66 we can substitute 21 for y to find that x + 21 = 66. Subtracting
\n" ); document.write( "21 from both sides we find that x = 66 - 21 = 45. So the larger of the two numbers
\n" ); document.write( "is 45.
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\n" ); document.write( "Hope this helps you to understand that two equations can be used to solve this problem
\n" ); document.write( "and gives you some insight into the substitution method of solving the set of two equations. \n" ); document.write( "