document.write( "Question 271438: Find two numbers such that twice the first exceeds three times the second by 1, and three times the first exceeds twice the second by 14. \n" ); document.write( "
Algebra.Com's Answer #198914 by ankor@dixie-net.com(22740)\"\" \"About 
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let x = the first number
\n" ); document.write( "let y = the second number
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each statement:
\n" ); document.write( ":
\n" ); document.write( "Find two numbers such that twice the first exceeds three times the second by 1,
\n" ); document.write( "2x = 3y + 1
\n" ); document.write( ":
\n" ); document.write( "and three times the first exceeds twice the second by 14.
\n" ); document.write( "3x = 2y + 14
\n" ); document.write( ":
\n" ); document.write( "Multiply the first equation by 2, and the 2nd equation by 3
\n" ); document.write( "4x = 6y + 2
\n" ); document.write( "9x = 6y + 42
\n" ); document.write( "---------------subtraction eliminates y, find x
\n" ); document.write( "-5x = -40
\n" ); document.write( "x = +8
\n" ); document.write( ":
\n" ); document.write( "Find y using the 1st equation
\n" ); document.write( "2(8) = 3y + 1
\n" ); document.write( "16 - 1 = 3y
\n" ); document.write( "3y = 15
\n" ); document.write( "y = 5
\n" ); document.write( ":
\n" ); document.write( "Check solution in the 2nd equation
\n" ); document.write( "3(8) = 2(5) + 14
\n" ); document.write( "24 = 10 + 14
\n" ); document.write( ":
\n" ); document.write( "Response to the comment
\n" ); document.write( "2x = 3y + 1 is exactly the same thing as 2x - 3y = 1
\n" ); document.write( "and
\n" ); document.write( "3x = 2y + 14 is exactly the same thing as 3x - 2y = 14
\n" ); document.write( ":
\n" ); document.write( "You can check the solutions in either equation, if you doubt it \n" ); document.write( "
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