document.write( "Question 1150743: Let a, b, and c be real numbers such that a - 7b + 8c = 4 and 8a + 4b - c = 7. Then a^2 - b^2 + c^2 is what? \n" ); document.write( "
Algebra.Com's Answer #772163 by greenestamps(13200)\"\" \"About 
You can put this solution on YOUR website!


\n" ); document.write( "We have three unknowns and only two equations, so we can't solve to find the values of a, b, and c. But the problem doesn't ask us to do that; it only asks us to find the value of a^2-b^2+c^2.

\n" ); document.write( "Use elimination between the two equations to eliminate a, giving you an equation relating b and c; then use elimination again to eliminate c, giving you an equation relating b and c.

\n" ); document.write( "Then use those expressions to evaluate a^2-b^2+c^2. It turns out all the variable terms cancel, leaving you with a numerical value for the expression.
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document.write( "   a - 7b + 8c = 4  [1]\r\n" );
document.write( "  8a + 4b -  c = 7  [2]\r\n" );
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document.write( "eliminate c....\r\n" );
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document.write( "   a - 7b + 8c =  4\r\n" );
document.write( " 64a +32b - 8c = 56\r\n" );
document.write( " ------------------\r\n" );
document.write( " 65a +25b      = 60\r\n" );
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document.write( " 13a + 5b = 12\r\n" );
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document.write( "  a = (12-5b)/13  [3]\r\n" );
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document.write( "eliminate a....\r\n" );
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document.write( "  8a -56b +64c = 32\r\n" );
document.write( "  8a + 4b -  c =  7\r\n" );
document.write( "  -----------------\r\n" );
document.write( "     -60b +65c = 25\r\n" );
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document.write( "  -12b+13c = 5\r\n" );
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document.write( "  c = (12b+5)/13  [4]\r\n" );
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document.write( "Use [3] and [4] to evaluate a^2-b^2+c^2.
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\n" ); document.write( "\n" ); document.write( "I'll leave that to you. All the variable terms cancel, leaving you with what you want -- a numerical value for a^2-b^2+c^2.
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