document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116265>Question 116265</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by graphing: x^2+y^2=25 and x-2y=-5\r<BR>\n" );
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document.write( "I graphed my circle and line perfectly<BR>\n" );
document.write( "but when it came to using either addition or substitution methods<BR>\n" );
document.write( "to find the solution set (where the line crosses the circle at two points)<BR>\n" );
document.write( "I had problems:(\r<BR>\n" );
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document.write( "I can see by looking at my graph that one solution is (-5,0) and the other<BR>\n" );
document.write( "is approximately (3.5, 4.5) but I have to use one of the above methods <BR>\n" );
document.write( "to show how I came up with my solutions and show my work.\r<BR>\n" );
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document.write( "This is what I've done so far:<BR>\n" );
document.write( "Using substitution method\r<BR>\n" );
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document.write( "x^2+y^2=25   and   x-2y=-5  (changed to x=2y-5) and substituted in to 1st equation<BR>\n" );
document.write( "(2y-5)^2+y^2=25<BR>\n" );
document.write( "4y^2-20y+25+y^2=25<BR>\n" );
document.write( "(combine like terms)<BR>\n" );
document.write( "5y^2-20y+25=25<BR>\n" );
document.write( "(subtract 25 from each side)<BR>\n" );
document.write( "5y^2-20y=0\r<BR>\n" );
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document.write( "This is where I loose it, because in class all of our problems worked out nice and neat<BR>\n" );
document.write( "and all I had to do was factor my quadratic equation to come up with one solution and<BR>\n" );
document.write( "then plug that into one of my original problems to get my second.<BR>\n" );
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document.write( "No one in study group tonight quite got this one either and this is due this Thursday! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84545 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=84545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Good Job ...<BR>\n" );
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document.write( "x^2+y^2=25   and   x-2y=-5  (changed to x=2y-5) and substituted in to 1st equation<BR>\n" );
document.write( "(2y-5)^2+y^2=25 <=== OK<BR>\n" );
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document.write( "4y^2-20y+25+y^2=25 <=== OK<BR>\n" );
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document.write( "(combine like terms)<BR>\n" );
document.write( "5y^2-20y+25=25 <=== OK<BR>\n" );
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document.write( "(subtract 25 from each side)<BR>\n" );
document.write( "5y^2-20y=0 <====<BR>\n" );
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document.write( "Now just factor 5y out of the two terms on the left side to get:<BR>\n" );
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document.write( "5y*(y - 4) = 0<BR>\n" );
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document.write( "This equation will be true if either of the two factors on the left side equals zero because<BR>\n" );
document.write( "a multiplication by zero on the left side makes the left side zero and, therefore, <BR>\n" );
document.write( "equal to the zero on the right side.<BR>\n" );
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document.write( "So there are two possible answers for y (because the line crosses the circle at two points).<BR>\n" );
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document.write( "Set the factors equal to zero ...<BR>\n" );
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document.write( "First:<BR>\n" );
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document.write( "5y = 0 ... divide both sides by 5 to get y = 0<BR>\n" );
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document.write( "Next:<BR>\n" );
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document.write( "y - 4 = 0 ... add 4 to both sides ...<BR>\n" );
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document.write( "y = 4<BR>\n" );
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document.write( "Plug these two values for y (0 and 4) into the equation x - 2y = -5. [Of the two equations this will <BR>\n" );
document.write( "probably be the easier one to work with.]<BR>\n" );
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document.write( "When y = 0 the equation x - 2y = -5 becomes x = -5. So (-5, 0) is one of the intersection<BR>\n" );
document.write( "points.<BR>\n" );
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document.write( "When y = 4 the equation x - 2y = -5 becomes x - (2*4) = -5 which simplifies to x - 8 = -5<BR>\n" );
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document.write( "Add 8 to both sides and you get x = +3. So the point (3, 4) is the second point at which the<BR>\n" );
document.write( "line crosses the circle.<BR>\n" );
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document.write( "You did a very good job on the hardest part of the problem ... you just needed a little hint<BR>\n" );
document.write( "at the very last part. Keep up the good work ... good luck to you and your study group.<BR>\n" );
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