document.write( "Question 839884: Solve each system by using the substitution method.\r
\n" ); document.write( "\n" ); document.write( "2x^2 - y^2 = 14\r
\n" ); document.write( "\n" ); document.write( "y - 2x = -4 \n" ); document.write( "

Algebra.Com's Answer #506008 by Fombitz(32388) $\"\"$ $\"About$

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The intersection of a straight line and a hyperbola,
\n" ); document.write( "1. $\"2x%5E2+-+y%5E2+=+14\"$
\n" ); document.write( "2. $\"y+-+2x+=+-4\"$
\n" ); document.write( "From eq. 2,
\n" ); document.write( " $\"y=2x-4\"$
\n" ); document.write( "Substitute into eq. 1,
\n" ); document.write( " $\"2x%5E2-%282x-4%29%5E2=14\"$
\n" ); document.write( " $\"2x%5E2-%284x%5E2-16x%2B16%29=14\"$
\n" ); document.write( " $\"2x%5E2-4x%5E2%2B16x-16=14\"$
\n" ); document.write( " $\"-2x%5E2%2B16x-30=0\"$
\n" ); document.write( " $\"x%5E2-8x%2B15=0\"$
\n" ); document.write( " $\"%28x-5%29%28x-3%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"x-5=0\"$
\n" ); document.write( " $\"x=5\"$
\n" ); document.write( "Then, $\"y=2x-4=2%285%29-4=10-4=6\"$ (5,6)
\n" ); document.write( "and
\n" ); document.write( " $\"x-3=0\"$
\n" ); document.write( " $\"x=3\"$
\n" ); document.write( "Then, $\"y=2x-4=2%283%29-4=6-4=2\"$ (3,2)
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