document.write( "Question 139467This question is from textbook College Algebra
\n" ); document.write( ": Hello, I worked this problem and only got half credit.
\n" ); document.write( "How can I work this as a systems of equations
\n" ); document.write( "x^2+y^2=25
\n" ); document.write( "5=x+y
\n" ); document.write( "This is what I did
\n" ); document.write( "x=5-y
\n" ); document.write( "(y-5)^2+y^2=25
\n" ); document.write( "2y-y^2-25=0 \n" ); document.write( "
Algebra.Com's Answer #101767 by solver91311(24713)\"\" \"About 
You can put this solution on YOUR website!
Think about what you would expect to get before you start working on anything. \"x%5E2%2By%5E2=25\" is a circle centered at the origin with a radius of 5. \"5=x%2By\" can be written as \"y=-x%2B5\" which is a straight line with a slope of -1 and a y-intercept of 5. So we have a straight line and a circle. You have one of three possible outcomes for such a situation. The line intersects the circle in two places, the line is tangent to the circle so it intersects in only one place, or the line doesn't intersect at all.\r
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\n" ); document.write( "\n" ); document.write( "Given that, your solution method was correct up to the point where you expanded the binomial and collected like terms. Your algebraic manipulation was faulty.\r
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\n" ); document.write( "\n" ); document.write( "\"%285-y%29%5E2=25-10y%2By%5E2\", so you should have gotten to \"25-10y%2By%5E2%2By%5E2-25=0\"\r
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\n" ); document.write( "\n" ); document.write( "\"2y%5E2-10y=0\"\r
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\n" ); document.write( "\n" ); document.write( "\"y%5E2-5y=y%28y-5%29=0\"\r
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\n" ); document.write( "\n" ); document.write( "So, \"y=0\" or \"y+=+5\". From here you can calculate the two x-coordinates to complete your points of intersection.\r
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\n" ); document.write( "\n" ); document.write( "The fact that you substituted \"y-5\" instead of \"5-y\" was an error but not one that would have an impact on the result. \"y-5=-%285-y%29\", and since you were squaring that quantity, the sign wouldn't matter in the final analysis. I can't for the life of me figure out how you got from \"%28y-5%29%5E2%2By%5E2=25\" to \"2y-y%5E2-25=0\", so my only advice is to go back and thoroughly review the FOIL process for expanding binomials.\r
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