document.write( "Question 144688: Solve the following simultaneous equation
\n" ); document.write( "32x^2+15y^2=2112
\n" ); document.write( "7x^2-3y^2=60
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Algebra.Com's Answer #105437 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Solve the following simultaneous equation
\n" ); document.write( "32x^2+15y^2 = 2112
\n" ); document.write( "7x^2 - 3y^2 = 60
\n" ); document.write( ":
\n" ); document.write( "Multiply the 2nd equation by 5 and add to the 1st equation
\n" ); document.write( "Solve the following simultaneous equation
\n" ); document.write( "32x^2 + 15y^2 = 2112
\n" ); document.write( "35x^2 - 15y^2 = 300
\n" ); document.write( "----------------------adding eliminates y
\n" ); document.write( "67x^2 = 2412
\n" ); document.write( "divide both sides by67
\n" ); document.write( "x^2 = 36
\n" ); document.write( "x = +/- $\"sqrt%2836%29\"$
\n" ); document.write( "x = +/-6
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\n" ); document.write( "Find y using the 2nd original equation:
\n" ); document.write( "7(36) - 3y^2 = 60
\n" ); document.write( "252 - 3y^2 = 60
\n" ); document.write( "-3y^2 = 60 - 252
\n" ); document.write( "-3y^2 = -192
\n" ); document.write( "3y^2 = +192
\n" ); document.write( "y^2 = $\"192%2F3\"$
\n" ); document.write( "y^2 = 64
\n" ); document.write( "y = +/-8
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\n" ); document.write( ":
\n" ); document.write( "Check solutions in 1st original equation
\n" ); document.write( ":
\n" ); document.write( "32(6^2) + 15(8^2) =
\n" ); document.write( "32(36) + 15(64) =
\n" ); document.write( "1152 + 960 = 2112
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