document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=958102>Question 958102</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The system of linear equations below has a unique solution for all but one value of a : <BR>\n" );
document.write( "10 x - 20 y = 50 <BR>\n" );
document.write( "26 x + a y = 130 \r<BR>\n" );
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document.write( "What is this exceptional value for a ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #585517 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=585517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 10x-20y=50 <BR>\n" );
document.write( "26x+ay=130<BR>\n" );
document.write( "If the two equations are equivalent, there are infinite solutions.<BR>\n" );
document.write( "Divide the coefficient of x in first equation by coefficient in second: 10/26=2.6<BR>\n" );
document.write( "Divide constant in first by constant in second: 50/130=2.6<BR>\n" );
document.write( "They are the same, so use this factor to determine coefficient of y<BR>\n" );
document.write( "(2.6)(20)=-52 <BR>\n" );
document.write( "This makes the second equation:<BR>\n" );
document.write( "26x+(-52)y=130 so a=-52 and both equations represent the same line, so there are infinite solutions.<BR>\n" );
document.write( "ANSWER: The exceptional value of a is (-52).\r<BR>\n" );
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