document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=397526>Question 397526</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the values of b and c for which the equations x+5y=4 and 2x+by=c have:<BR>\n" );
document.write( "A unique solution, an infinite set of solutions and no solution. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #281741 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=281741\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The system can be represented in augmented matrix form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C3%2C1%2C5%2C4%2C2%2Cb%2Cc%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C3%2C1%2C5%2C4%2C2%2Cb%2Cc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Multiplying the 1st row by -2 and then adding to the 2nd gives the new matrix\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C3%2C1%2C5%2C4%2C0%2Cb+-+10%2Cc+-+8%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C3%2C1%2C5%2C4%2C0%2Cb+-+10%2Cc+-+8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Hence for infinitely many solutions, b = 10 and c = 8;<BR>\n" );
document.write( "for no solution, b = 10 and c not equal to 8;<BR>\n" );
document.write( "for unique solution, b should be not equal to 10. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );