document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1009252>Question 1009252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simultaneous equations - one linear, one quadratic <BR>\n" );
document.write( "Solve the following equations:\r<BR>\n" );
document.write( "\n" );
document.write( "xy = 12<BR>\n" );
document.write( "x + y = 7 \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #624756 by </B><A HREF=/tutors/aboutme.mpl?userid=epistrophy990><B>epistrophy990(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=epistrophy990><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=624756\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> xy=12  (equation 1)<BR>\n" );
document.write( "x+y=7  (equation 2)\r<BR>\n" );
document.write( "\n" );
document.write( "divide equation 1, both sides, by -X --> -y= -12/x  --> Y = 12/x  (mult by -1)\r<BR>\n" );
document.write( "\n" );
document.write( "Substitute Y = 12X into equation 2  for Y \r<BR>\n" );
document.write( "\n" );
document.write( "a) X + 12/X =7          (substituting 12X for Y into equation 2)<BR>\n" );
document.write( "b) X + 12/X - 7 = 0     (subtract 7 from both sides)<BR>\n" );
document.write( "C) X(X +12/X -7) = x(0)  (Multiply both sides by X)<BR>\n" );
document.write( "   X^2 + 12 - 7x  = 0    (distribute)\r<BR>\n" );
document.write( "\n" );
document.write( "d) (x-3)(X-4) = 0        (factor)<BR>\n" );
document.write( "e) Set x-3 =0  and x-4 =0<BR>\n" );
document.write( "f)  Therefore there are 2 solutions for X : x=3 and x=4\r<BR>\n" );
document.write( "\n" );
document.write( "g) Take the first value of X=3 and substitute for X in Equation 2:\r<BR>\n" );
document.write( "\n" );
document.write( "h) 3 +y =7 --> Y = 4  Therefore there is an intersection at (3,4)<BR>\n" );
document.write( "i)  Take the second value of X=4 and substitute into Equation 2<BR>\n" );
document.write( "j) 4 + Y =7 ---> Y = 3  Therefore there is an intersection at (4,3)\r<BR>\n" );
document.write( "\n" );
document.write( "k)  Substitute the 2 solutions back into both equations to make sure there are no extraneous equations.\r<BR>\n" );
document.write( "\n" );
document.write( "l) 3+4 =7 : 4+3 =7  (Equation 2)<BR>\n" );
document.write( "m) 3*4 =7 : 4*3 =7   (equation 1)\r<BR>\n" );
document.write( "\n" );
document.write( "Therefore the solutions are  (3,4) and (4,3)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );