document.write( "Question 173597: \"system%28%281%2F2%29%5E%28x%2By%29=16%2C+log%28x-y%2C8%29=-3%29\". Calculate the values of x and y \n" ); document.write( "
Algebra.Com's Answer #129388 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\"system%28%281%2F2%29%5E%28x%2By%29=16%2C+log%28x-y%2C8%29=-3%29\". Calculate the values of x and y
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document.write( "Let's simplify the equations.\r\n" );
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document.write( "Simplifying the first equation:\r\n" );
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document.write( "\"matrix%281%2C3%2C%281%2F2%29%5E%28x%2By%29%2C%22=%22%2C16%29\"\r\n" );
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document.write( "Write \"%281%2F2%29\" as \"%282%5E%28-1%29%29\"\r\n" );
document.write( "And write \"16\" as \"2%5E4\"\r\n" );
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document.write( "\"matrix%281%2C3%2C%282%5E%28-1%29%29%5E%28x%2By%29%2C%22=%22%2C2%5E4%29\"\r\n" );
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document.write( "Remove the parentheses by multiplying the\r\n" );
document.write( "inner exponent \"-1\" by the outer\r\n" );
document.write( "exponent \"x%2By\", getting \"-x-y\"\r\n" );
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document.write( "\"matrix%281%2C3%2C2%5E%28-x-y%29%2C%22=%22%2C2%5E4%29\"\r\n" );
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document.write( "The base on each side is the same\r\n" );
document.write( "positive number, which is not 1, so\r\n" );
document.write( "we may equate the exponents:\r\n" );
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document.write( "\"matrix%281%2C3%2C+-x-y%2C+%22=%22%2C+4%29\"\r\n" );
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document.write( "Let's multiply every term by \"-1\"\r\n" );
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document.write( "\"matrix%281%2C3%2C+x%2By%2C+%22=%22%2C-4%29\"\r\n" );
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document.write( "------\r\n" );
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document.write( "Now we simplify the second equation:\r\n" );
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document.write( "\"log%28x-y%2C8%29=-3\"\r\n" );
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document.write( "Use the rule of logs:  \"log%28B%2CC%29=A\" can be rewritten \"B%5EA=C\"\r\n" );
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document.write( "\"matrix%281%2C3%2C%28x-y%29%5E%28-3%29%2C+%22=%22%2C+8%29\"\r\n" );
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document.write( "Write \"8\" as \"2%5E3\"\r\n" );
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document.write( "\"matrix%281%2C3%2C%28x-y%29%5E%28-3%29%2C+%22=%22%2C+2%5E3%29\"\r\n" );
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document.write( "Enclose both sides in parentheses and raise to the\r\n" );
document.write( "\"1%2F3\" power:\r\n" );
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document.write( "Multiply inner exponents by outer exponents:\r\n" );
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document.write( "\"matrix%281%2C3%2C%28x-y%29%5E%28-1%29%2C+%22=%22%2C+2%5E1%29\" \r\n" );
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document.write( "Write the left side as \"1%2F%28x-y%29\" and right side as just \"2\" \r\n" );
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document.write( "\"matrix%281%2C3%2C1%2F%28x-y%29%2C+%22=%22%2C+2%29\"\r\n" );
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document.write( "Multiply both sides by \"%28x-y%29\"\r\n" );
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document.write( "\"matrix%281%2C3%2C1%2C+%22=%22%2C+2%28x-y%29%29\"\r\n" );
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document.write( "\"matrix%281%2C3%2C1%2C+%22=%22%2C+2x-2y%29\"\r\n" );
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document.write( "Put the right side on the left and vice-versa:\r\n" );
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document.write( "\"matrix%281%2C3%2C2x-2y%2C+%22=%22%2C+1%29\"\r\n" );
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document.write( "------\r\n" );
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document.write( "So we now have this simpler system of equations:\r\n" );
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document.write( "\"system%28x%2By=-4%2C+2x-2y=1%29\"\r\n" );
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document.write( "I assume you know how to solve that system.\r\n" );
document.write( "If you don't, post again asking how:\r\n" );
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document.write( "Answer:  \"matrix%281%2C3%2Cx=-7%2F4%2C+%22%2C%22%2C+y=-9%2F4%29\"\r\n" );
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document.write( "Edwin
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