document.write( "Question 1126072: If x - y = 14 and x^2 - y^2 = 84, then what is the value of x \n" ); document.write( "

Algebra.Com's Answer #742379 by rothauserc(4718) $\"\"$ $\"About$

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1) x - y = 14
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\n" ); document.write( "2) x^2 - y^2 = 84
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\n" ); document.write( "factor equation 2
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\n" ); document.write( "(x+y) * (x-y) = 84
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\n" ); document.write( "substitute for (x-y) using equation 1
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\n" ); document.write( "(x+y) * 14 = 84
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\n" ); document.write( "x + y = 84/14 = 6
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\n" ); document.write( "3) x + y = 6
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\n" ); document.write( "add equations 1 and 3
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\n" ); document.write( "2x = 20
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\n" ); document.write( "x = 10 and y = -4
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\n" ); document.write( "check the answers in equations 1 and 2
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\n" ); document.write( "equation 1
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\n" ); document.write( "10 - (-4) = 14
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\n" ); document.write( "14 = 14
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\n" ); document.write( "equation 2
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\n" ); document.write( "10^2 - (-4)^2 = 84
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\n" ); document.write( "100 - 16 = 84
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\n" ); document.write( "84 = 84
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