document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181781>Question 181781</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I'm having trouble with the following questions:\r<BR>\n" );
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document.write( "For what value of 'a' is there no unique solution for the following?\r<BR>\n" );
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document.write( "3x - 2y = 5<BR>\n" );
document.write( "5x + ay = 4\r<BR>\n" );
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document.write( "Also, when 'a' has this value, is there an infinite number of solutions or no solution? Justify your answer.\r<BR>\n" );
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document.write( "Thank you so much!\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136379 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=136379\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "3x - 2y = 5------eq1<BR>\n" );
document.write( "5x + ay = 4 -----eq2<BR>\n" );
document.write( "Put eq1 and eq2 in slope -intercept form (y=mx+b)<BR>\n" );
document.write( "eq1:<BR>\n" );
document.write( "-2y=5-3x  divide each side by -2<BR>\n" );
document.write( "y=(3/2)x-5/2-------------------------eq1 in slope-intercept form<BR>\n" );
document.write( "eq2:<BR>\n" );
document.write( "ay=4-5x divide each side by a<BR>\n" );
document.write( "y=(-5/a)x+4/a--------------------------eq2 in slope-intercept form\r<BR>\n" );
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document.write( "If eq1 and eq2 have the same slope, they are either parallel (no solutions) or lay on top of each other (infinite solutions), so:<BR>\n" );
document.write( "(-5/a)=3/2  multiply each side by 2a<BR>\n" );
document.write( "-10=3a a=-10/3<BR>\n" );
document.write( "Substitute a=-10/3 into eq2:<BR>\n" );
document.write( "y=(-5/(-10/3)x+4/(-10/3) simplify<BR>\n" );
document.write( "y=(3/2)x-6/5  ------------------------------eq2a<BR>\n" );
document.write( "Now if we compare eq1 and eq2a, we see that they have the same slope but not the same y-intercept which means that if a=-(10/3) the lines are parallel and there is no solution.\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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