document.write( "Question 1007316: Given the equation of the circle $\"+x%5E2+%2By%5E2=25+\"$ and the equation of the line $\"+2x%2By=10\"$ ... Find the solutions algebraically. I don't get what we're supposed to do with those equations, add them, multiply, or what? \n" ); document.write( "

Algebra.Com's Answer #623276 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Given the equation of the circle x^2 + y^2 = 25 and
\n" ); document.write( " the equation of the line 2x + y = 10...
\n" ); document.write( " Find the solutions algebraically
\n" ); document.write( ":
\n" ); document.write( "One way is write the 2nd equation as
\n" ); document.write( "y = -2x + 10
\n" ); document.write( "Substitute for y in the 1st equation
\n" ); document.write( "x^2 + (-2x+10)^2 = 25
\n" ); document.write( "FOIL (-2x+10(-2x+10)
\n" ); document.write( "x^2 + (4x^2 - 20x -20x + 100) = 25
\n" ); document.write( "Combine like terms
\n" ); document.write( "x^2 + 4x^2 - 40x + 100 - 25 = 0
\n" ); document.write( "5x^2 - 40x + 75 = 0
\n" ); document.write( "Simplify, divide by 5
\n" ); document.write( "x^2 - 8x + 15 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(x-5)(x-3) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "x = 5
\n" ); document.write( "x = 3
\n" ); document.write( ":
\n" ); document.write( "Using the equation y = -2x+10, find y using both x solution
\n" ); document.write( "y = -2(5) + 10
\n" ); document.write( "y = 0
\n" ); document.write( "and
\n" ); document.write( "y = -2(3) + 10
\n" ); document.write( "y = -6 + 10
\n" ); document.write( "y = 4
\n" ); document.write( ":
\n" ); document.write( "Solutions:
\n" ); document.write( " x=5; y=0
\n" ); document.write( " x=3; y=4
\n" ); document.write( ":
\n" ); document.write( "Check in the 1st equation using the last pair, (the first pair is obvious)
\n" ); document.write( "3^2 + 4^2 = 25
\n" ); document.write( "9 + 16 = 25
\n" ); document.write( " \n" ); document.write( "

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