document.write( "Question 573236: I am having trouble solving a system of equations:\r
\n" ); document.write( "\n" ); document.write( " $\"4sqrt%28x%5E2-3x%29+-+3sqrt%28y%5E2%2B6y%29=+-4\"$
\n" ); document.write( " $\"sqrt%28x%5E2-3x%29+%2B+sqrt%28y%5E2%2B6y%29=+6\"$ \r
\n" ); document.write( "\n" ); document.write( "I squared both sides to remove the radical:
\n" ); document.write( " $\"16%28x%5E2-3x%29+-9%28y%5E2%2B6y%29=16\"$
\n" ); document.write( " $\"x%5E2-3x%2By%5E2%2B6y=36\"$ \r
\n" ); document.write( "\n" ); document.write( "and that is as far as I've gotten. \r
\n" ); document.write( "\n" ); document.write( "thanks
\n" ); document.write( "lpkitty \n" ); document.write( "

Algebra.Com's Answer #368781 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"4sqrt%28x%5E2-3x%29+-+3sqrt%28y%5E2%2B6y%29=+-4\"$
\n" ); document.write( " $\"sqrt%28x%5E2-3x%29+%2B+sqrt%28y%5E2%2B6y%29=+6\"$
\n" ); document.write( "But these are like terms so let's simplify things by using elimination
\n" ); document.write( "Multipl the 2nd equation by 3, add to the 1st equation
\n" ); document.write( " $\"4sqrt%28x%5E2-3x%29+-+3sqrt%28y%5E2%2B6y%29=+-4\"$
\n" ); document.write( " $\"3sqrt%28x%5E2-3x%29+%2B+3sqrt%28y%5E2%2B6y%29=+18\"$
\n" ); document.write( "-----------------------------------adding eliminates the y radical, so we have
\n" ); document.write( " $\"7sqrt%28x%5E2-3x%29+=+14\"$
\n" ); document.write( "divide both sides by 7
\n" ); document.write( " $\"sqrt%28x%5E2-3x%29+=+2\"$
\n" ); document.write( "square both sides
\n" ); document.write( "x^2 - 3x = 4
\n" ); document.write( "x^2 - 3x - 4 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(x-4)(x+1) = 0
\n" ); document.write( "two solutions
\n" ); document.write( "x = -1
\n" ); document.write( "x = 4
\n" ); document.write( ":
\n" ); document.write( "Use the 2nd original equation to find y
\n" ); document.write( " $\"sqrt%28x%5E2-3x%29+%2B+sqrt%28y%5E2%2B6y%29=+6\"$
\n" ); document.write( " $\"sqrt%284%5E2-3%284%29%29+%2B+sqrt%28y%5E2%2B6y%29=+6\"$
\n" ); document.write( " $\"sqrt%284%29+%2B+sqrt%28y%5E2%2B6y%29=+6\"$
\n" ); document.write( " $\"2+%2B+sqrt%28y%5E2%2B6y%29=+6\"$
\n" ); document.write( " $\"sqrt%28y%5E2%2B6y%29=+6-2\"$
\n" ); document.write( " $\"sqrt%28y%5E2%2B6y%29=+4\"$
\n" ); document.write( "square both sides
\n" ); document.write( "y^2 + 6y = 16
\n" ); document.write( "y^2 + 6y - 16 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(y+8)(y-2) = 0
\n" ); document.write( "Y = -8
\n" ); document.write( "Y = 2
\n" ); document.write( ":
\n" ); document.write( "You should check all the solutions in the original equations\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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