document.write( "Question 300288: Solve the following system.\r
\n" ); document.write( "\n" ); document.write( "x2 + y 2= 25
\n" ); document.write( "2x + y = 10\r
\n" ); document.write( "\n" ); document.write( "The solution set {(-, ), (, )}.
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Algebra.Com's Answer #215498 by Fombitz(32388) $\"\"$ $\"About$

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The solution to this system solves the intersection of a circle and a line.
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\n" ); document.write( "1. $\"x%5E2%2By%5E2=25\"$
\n" ); document.write( "2. $\"2x%2By=10\"$
\n" ); document.write( "From eq. 2,
\n" ); document.write( " $\"y=-2x%2B10\"$
\n" ); document.write( " $\"y%5E2=%28-2x%2B10%29%5E2\"$
\n" ); document.write( " $\"y%5E2=4x%5E2-40x%2B100\"$
\n" ); document.write( "Substitute into eq. 1,
\n" ); document.write( " $\"x%5E2%2By%5E2=25\"$
\n" ); document.write( " $\"x%5E2%2B4x%5E2-40x%2B100=25\"$
\n" ); document.write( " $\"5x%5E2-40x%2B100=25\"$
\n" ); document.write( " $\"5x%5E2-40x%2B75=0\"$
\n" ); document.write( " $\"x%5E2-8x%2B15=0\"$
\n" ); document.write( "Factor,
\n" ); document.write( " $\"%28x-3%29%28x-5%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"x-3=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=3\"$ \r
\n" ); document.write( "\n" ); document.write( "Then using eq. 2,
\n" ); document.write( " $\"+2x%2By=10\"$
\n" ); document.write( " $\"6%2By=10\"$
\n" ); document.write( " $\"y=4\"$
\n" ); document.write( "(3,4)
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\n" ); document.write( " $\"x-5=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"10%2By=10+\"$
\n" ); document.write( " $\"y=0\"$
\n" ); document.write( "(5,0)
\n" ); document.write( "The solution is verified by the previous graph. \n" ); document.write( "

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