document.write( "Question 197117: Solve the following system of equations algebraically:
\n" ); document.write( "x^2+y^2=100
\n" ); document.write( "y=x-2 \n" ); document.write( "
Algebra.Com's Answer #147805 by ankor@dixie-net.com(22740)\"\" \"About 
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Solve the following system of equations algebraically:
\n" ); document.write( "x^2+y^2=100
\n" ); document.write( "y = (x-2)
\n" ); document.write( ";
\n" ); document.write( "Substitute (x-2) for y in the 1st equation:
\n" ); document.write( "x^2 + (x-2)^2 = 100
\n" ); document.write( ":
\n" ); document.write( "FOIL (x-2)(x-2)
\n" ); document.write( "x^2 + (x^2 - 4x + 4) = 100
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\n" ); document.write( "Arrange as a quadratic equation:
\n" ); document.write( "2x^2 - 4x + 4 - 100 = 0
\n" ); document.write( ":
\n" ); document.write( "2x^2 - 4x - 96 = 0
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "x^2 - 2x - 48 = 0
\n" ); document.write( "Factor to:
\n" ); document.write( "(x-8)(x+6) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "x = +8
\n" ); document.write( "and
\n" ); document.write( "x = -6
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\n" ); document.write( "Find y when x = 8
\n" ); document.write( "y = 8 - 2
\n" ); document.write( "y = 6
\n" ); document.write( ":
\n" ); document.write( "Find y when x = -6
\n" ); document.write( "y = -6 - 2
\n" ); document.write( "y = -8
\n" ); document.write( ":
\n" ); document.write( "Check both solutions in the first equation
\n" ); document.write( "x=8, y = 6
\n" ); document.write( "8^2 + 6^2 =
\n" ); document.write( "64 + 36 = 100
\n" ); document.write( "and
\n" ); document.write( "x = -6, y = -8
\n" ); document.write( "-6^2 + -8^2 =
\n" ); document.write( "+36 + 64 = 100
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