document.write( "Question 76853: solve the sytem algebraically\r
\n" ); document.write( "\n" ); document.write( "y^2 = x^2 - 32
\n" ); document.write( "x^2 + y^2 = 40 \n" ); document.write( "

Algebra.Com's Answer #55094 by funmath(2933) $\"\"$ $\"About$

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solve the sytem algebraically\r
\n" ); document.write( "\n" ); document.write( "y^2 = x^2 - 32
\n" ); document.write( "x^2 + y^2 = 40
\n" ); document.write( "Substitute x^2-32 in for y^2 in the second equation.
\n" ); document.write( " $\"x%5E2%2B%28x%5E2-32%29=40\"$
\n" ); document.write( " $\"2x%5E2-32=40\"$
\n" ); document.write( " $\"2x%5E2-32%2B32=40%2B32\"$
\n" ); document.write( " $\"2x%5E2=72\"$
\n" ); document.write( " $\"2x%5E2%2F2=72%2F2\"$
\n" ); document.write( " $\"x%5E2=36\"$
\n" ); document.write( " $\"sqrt%28x%5E2%29=%2B-sqrt%2836%29\"$
\n" ); document.write( "x=-6 or x=6
\n" ); document.write( "Let x=-6 or x=6 (They will both have the same outcome because x is squared.) in the first equation and solve for y.
\n" ); document.write( " $\"y%5E2=%28-6%29%5E2-32\"$
\n" ); document.write( " $\"y%5E2=36-32\"$
\n" ); document.write( " $\"y%5E2=4\"$
\n" ); document.write( " $\"sqrt%28y%5E2%29=%2B-sqrt%284%29\"$
\n" ); document.write( "y=-2 or y=2
\n" ); document.write( "Therefore two solutions are (-6,-2) and (-6,2)
\n" ); document.write( " $\"y%5E2=%286%29%5E2-32\"$
\n" ); document.write( " $\"y%5E2=36-32\"$
\n" ); document.write( " $\"y%5E2=4\"$
\n" ); document.write( " $\"sqrt%28y%5E2%29=%2B-sqrt%284%29\"$
\n" ); document.write( "y=-2 or y=2
\n" ); document.write( "Therefore two solutions are (6,-2) and (6,2)
\n" ); document.write( "There are four solutions: (-6,-2), (-6,2), (6,-2), and (6,2)
\n" ); document.write( "It helps to look at the graph.
\n" ); document.write( "Graphically it looks like this:
\n" ); document.write( "

\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "

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