document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=932611>Question 932611</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the system of equations <BR>\n" );
document.write( "3x + 4y = 8<BR>\n" );
document.write( "6x + ty = s<BR>\n" );
document.write( "where t and s are real numbers, find values of s and t so that the system has exactly one solution </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #566263 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=566263\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3x + 4y = 8<BR>\n" );
document.write( "6x + ty = s<BR>\n" );
document.write( "---<BR>\n" );
document.write( "4y = -3x + 8<BR>\n" );
document.write( "y = (-3/4)x + 2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "ty = -6x + s<BR>\n" );
document.write( "y = (-6/t)x + s/t<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = (-3/4)x + 2<BR>\n" );
document.write( "y = (-6/t)x + s/t<BR>\n" );
document.write( "---<BR>\n" );
document.write( "choose t so the slopes are perpendicular ...<BR>\n" );
document.write( "note that perpendicular lines have negative reciprocal slopes:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "-6/t = -1/(-3/4)<BR>\n" );
document.write( "6/t = 1/(-3/4)<BR>\n" );
document.write( "t = 6*(-3/4)<BR>\n" );
document.write( "t = -4.5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "choose s so the y-intercept (s/t) is a nice whole number:<BR>\n" );
document.write( "s/t<BR>\n" );
document.write( "s/(-4.5)<BR>\n" );
document.write( "if s = 4.5 then s/t = -1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "s = 4.5<BR>\n" );
document.write( "t = -4.5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "3x + 4y = 8<BR>\n" );
document.write( "6x - 4.5y = 4.5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "put the system of linear equations into standard form<BR>\n" );
document.write( "---<BR>\n" );
document.write( "3x + 4y = 8<BR>\n" );
document.write( "6x - 4.5y = 4.5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "copy and paste the above standard form linear equations in to this solver:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "solution:<BR>\n" );
document.write( "x = 1.44<BR>\n" );
document.write( "y = 0.92<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the system has exactly one solution ...<BR>\n" );
document.write( "the above choice of s and t satisfies the problem statement<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve systems of linear equations up to 6-equations 6-variables:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php<BR>\n" );
document.write( "--- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );