document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=409847>Question 409847</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My teacher gave me the system of equations to solve symbolically for intersections  x^2 + 4y^2 = 25, and x +2y = 7<BR>\n" );
document.write( "I tried to solve it, but got stuck. The answer I eventually got was very different then the answer he gave me, which was (3,2) and (4, 1.5).  He then refused to explain how he got that answer.  Can you help explain how to do this problem correctly? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #288361 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=288361\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Square the linear equation, giving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4xy+%2B+4y%5E2+=+49 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4xy+%2B+4y%5E2+=+49\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Subtract the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4y%5E2+=+25 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4y%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the preceding equation, to get 4xy = 24, or xy = 6, or y = 6/x.<BR>\n" );
document.write( "Then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4%286%2Fx%29%5E2+=+25 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4%286%2Fx%29%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2++%2B+144%2Fx%5E2+=+25 ALIGN=MIDDLE  ALT=\"x%5E2++%2B+144%2Fx%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4++-+25x%5E2+%2B+144+=+0 ALIGN=MIDDLE  ALT=\"x%5E4++-+25x%5E2+%2B+144+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+16%29%28x%5E2+-+9%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+16%29%28x%5E2+-+9%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> x = 4, -4, 3, -3<BR>\n" );
document.write( "The graph of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4y%5E2+=+25 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4y%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an ellipse with vertices (-5,0) and (5,0); and co-vertices (0, 5/2) and (0, -5/2).  The graph of  x +2y = 7 is a line with slope -1/2 and y-intercept 7/2.  The two graphs intersect only at two points (with both x-coordinates positive).  Hence the intersection points are:<BR>\n" );
document.write( "When x = 4, y = 6/4 = 3/2 ==> (4, 1.5).<BR>\n" );
document.write( "When x = 3, y = 6/3 = 2 ==> (3,2).\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );