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A negative number is 5 less than a second negative number. If the second number is multiplied by 2 less than the first, the product equals 8. Find the numbers.
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\n" ); document.write( "Let x = \"the negative 1st number\"
\n" ); document.write( "Let y = \"the negative 2nd number\"
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\n" ); document.write( "Write an equation for each statement:
\n" ); document.write( "\"A negative number is 5 less than a second negative number.\"
\n" ); document.write( "x = (y - 5)
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\n" ); document.write( "\" If the second number is multiplied by 2 less than the first, the product equals 8.\"
\n" ); document.write( "y * (x-2) = 8
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\n" ); document.write( " Find the numbers.
\n" ); document.write( "Substitute (y-5) for x in the above equation:
\n" ); document.write( "y * ((y-5)-2) = 8
\n" ); document.write( "y * (y - 7) = 8
\n" ); document.write( "y^2 - 7y = 8
\n" ); document.write( "y - 7y - 8 = 0
\n" ); document.write( "Factors to:
\n" ); document.write( "(y-8)(y+1) = 0
\n" ); document.write( "y = -1 is the solution we want
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\n" ); document.write( "Find x using the 1st equation, substitute -1 for y:
\n" ); document.write( "x = -1 - 5
\n" ); document.write( "x = -6
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\n" ); document.write( "Our two negative numbers are -6 and -1
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\n" ); document.write( "Check solution in the statement:
\n" ); document.write( "\"the second number is multiplied by 2 less than the first, the product equals 8.
\n" ); document.write( "-1 * (-6 -2) =
\n" ); document.write( "-1 * -8 = +8 \n" ); document.write( "