document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=398712>Question 398712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,<BR>\n" );
document.write( "I have linear equation problem that I am stuck on. I have tried the problem myself but I'm having trouble with it. Here is the problem I'm working on:\r<BR>\n" );
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document.write( "Determine the necessary conditions on a, b and c for the following systems to have:<BR>\n" );
document.write( "a unique solution; an infinite number of solutions; or be inconsistent.\r<BR>\n" );
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document.write( "x1 + ax2 = 5<BR>\n" );
document.write( "3x1 + 6x2 = b\r<BR>\n" );
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document.write( "Here is the work I've done so far, and this is all in matrices so imagine the boxes around the numbers:<BR>\n" );
document.write( "1 a |5<BR>\n" );
document.write( "3 6 |b\r<BR>\n" );
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document.write( "multiplying row 2 by 1/3<BR>\n" );
document.write( "1 a    | 5<BR>\n" );
document.write( "1 2    | b/3\r<BR>\n" );
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document.write( "subtracting row 1 from row 2<BR>\n" );
document.write( "1 a     |5<BR>\n" );
document.write( "0 2-a   |b/3 - 5\r<BR>\n" );
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document.write( "I'm not sure if what I've done is correct, but this is where I'm stuck because I do not know how to set up the three conditions?<BR>\n" );
document.write( "Thank you for any help<BR>\n" );
document.write( "Yury </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #282433 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=282433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine the necessary conditions on a, b and c for the following systems to have:<BR>\n" );
document.write( "a unique solution; an in finite number of solutions; or be inconsistent. <BR>\n" );
document.write( "x1 + ax2 = 5<BR>\n" );
document.write( "3x1 + 6x2 = b<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Put in slope-intercept form:<BR>\n" );
document.write( "x1 = -ax2 + 5<BR>\n" );
document.write( "slope = -a<BR>\n" );
document.write( "int = 5<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "x1 = -2x2 - (b/3)<BR>\n" );
document.write( "slope = -2<BR>\n" );
document.write( "int = (-b/3)<BR>\n" );
document.write( "============================ <BR>\n" );
document.write( "Unique solution when slopes are not equal:<BR>\n" );
document.write( "-a is not equal to -2<BR>\n" );
document.write( "a is not equal to 2<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Inconsistent when slopes are equal.<BR>\n" );
document.write( "-a = -2<BR>\n" );
document.write( "a = 2<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Infinite # of solutions when slopes and int are equal.<BR>\n" );
document.write( "a=2 <BR>\n" );
document.write( "and (-b/3) = 5<BR>\n" );
document.write( "b = -15<BR>\n" );
document.write( "===================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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