document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=726814>Question 726814</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Stuck and need help on solving this \r<BR>\n" );
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document.write( "7x-8y=24<BR>\n" );
document.write( "xy^2=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #444860 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=444860\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given;<BR>\n" );
document.write( "(1) x*y^2 = 1 and<BR>\n" );
document.write( "(2) 7x - 8y = 24<BR>\n" );
document.write( "Solve by substitution. Solve (1) for x and get<BR>\n" );
document.write( "(3) x = 1/(y^2); y not equal to zero.<BR>\n" );
document.write( "Place (3) into (2) and get<BR>\n" );
document.write( "(4) 7/(y^2) - 8y - 24 = 0<BR>\n" );
document.write( "Multiply (4) by y^2 and get<BR>\n" );
document.write( "(5) 7 - 8y^3 - 24y^2 =0 or<BR>\n" );
document.write( "(6) 8y^3 + 24y^2 - 7 = 0<BR>\n" );
document.write( "We know that (6) has one real root because it is an odd power equation in y. To get the real root I set the last two terms equal to zero and solve for y. This gives us<BR>\n" );
document.write( "(7) 24y^2 - 7 = 0 or<BR>\n" );
document.write( "(8) y^2 = 7/24 which is approximately<BR>\n" );
document.write( "(9) y = 1/2<BR>\n" );
document.write( "To check this trial value of y, place it into (6) and get<BR>\n" );
document.write( "(10) 8*(1/2)^2 + 24*(1/2)^2 - 7 = 0 or<BR>\n" );
document.write( "(11) 1 + 6 - 7 = 0<BR>\n" );
document.write( "Therefore<BR>\n" );
document.write( "(12) (y-1/2)<BR>\n" );
document.write( "is a factor of (6). Now use long division of (6) divided by (12) to get<BR>\n" );
document.write( "(13) 8y^2 + 28y + 14 = 0 or<BR>\n" );
document.write( "(14) 4y^2 + 14y + 7 = 0<BR>\n" );
document.write( "The roots of (14) are<BR>\n" );
document.write( "(15) y = {(-7+sqrt(21))/4,(-7-sqrt(21))/4}<BR>\n" );
document.write( "To get the corresponding values of x, substitute each of the three values of y given by (9), and (14) into (1) and get<BR>\n" );
document.write( "(16) x = 1/(1/2)^2 or<BR>\n" );
document.write( "(17) x = 4 and <BR>\n" );
document.write( "(18) x = {8/(35-7*sqrt(21)), 8/(35 + 7*sqrt(21))}<BR>\n" );
document.write( "I'll check (4,1/2) in (2).<BR>\n" );
document.write( "Is (7*4 - 8*(1/2) = 24)?<BR>\n" );
document.write( "Is (28 - 4 = 24)?<BR>\n" );
document.write( "Is (24 = 24)? Yes<BR>\n" );
document.write( "Answer: The three solution pairs are<BR>\n" );
document.write( "1) (4,1/2),<BR>\n" );
document.write( "2) (8/(35-7*sqrt(21)),((-7+sqrt(21))/4), and<BR>\n" );
document.write( "3) (8/(35+7*sqrt(21)),((-7-sqrt(21))/4})<BR>\n" );
document.write( "P.S. I checked 2) and 3) off line. They're OK.<BR>\n" );
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