document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=605884>Question 605884</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm trying to classify the system and determine the number solutions without graphing<BR>\n" );
document.write( "-5x-2y=10<BR>\n" );
document.write( "-10x-4y=20\r<BR>\n" );
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document.write( "A. Consistent, dependent<BR>\n" );
document.write( "B. consistent , independent<BR>\n" );
document.write( "C. Inconsistent<BR>\n" );
document.write( "D. None of these\r<BR>\n" );
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document.write( "Email llthomas83@yahoo.com </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #381837 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=381837\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let z = -5x-2y\r<BR>\n" );
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document.write( "Notice that 2z = 2(-5x-2y) = -10x-4y\r<BR>\n" );
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document.write( "So we can replace the left hand side of the first equation with 'z'. We can also replace the left hand side of the second equation with '2z'\r<BR>\n" );
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document.write( "This gives us the equations\r<BR>\n" );
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document.write( "z = 10\r<BR>\n" );
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document.write( "2z = 20\r<BR>\n" );
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document.write( "If we solve the second equation for z, we do indeed get z = 10.\r<BR>\n" );
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document.write( "This tells us that there are an infinite number of solutions. This is because the system we're given basically boils down to -5x-2y=10, which has an infinite number of solutions.\r<BR>\n" );
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document.write( "So this means that the system is consistent and dependent. </SPAN>\n" );
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