document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106372>Question 106372</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello out there,I really need some help with some problems,the first one is,State whether the system is consistent and independent,consistent and dependent,or inconsistent:4x+2y=8 and 2x+y=1.The next one is,State whether the system is consistent and independent,consistent and dependent,or inconsistent:x+y=4 and 2x-y=-7.The third one is,Determine whether the system has one solution,no solution,or infinitely many solutions:y=-x+2 and 3x+3y=6.And the last one is,Determine whether the system has one solution,no solution,or infinitely many solutions:y=2/3x and 2x-y=-4.Thanks to whoever can help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77484 by </B><A HREF=/tutors/aboutme.mpl?userid=elima><B>elima(1433)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=elima><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=77484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4x+2y=8<BR>\n" );
document.write( "2x+y=1<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "We will solve this by elimination since you don't say which to use;<BR>\n" );
document.write( "1)4x+2y=8<BR>\n" );
document.write( "2)2x+y=1<BR>\n" );
document.write( "we will multiply a -2 to the second equation to eliminate the y;<BR>\n" );
document.write( "(-2)2x+y=1<BR>\n" );
document.write( "-4x-2y=1<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Now lets add the two equations together;<BR>\n" );
document.write( "4x+2y=8<BR>\n" );
document.write( "-4x-2y=-2<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "0=-2<BR>\n" );
document.write( "Since this is o=-2, it is inconsistent<BR>\n" );
document.write( "==============================================<BR>\n" );
document.write( "With this next one, when you add them together they already eliminate a variable, so no other multiplying is necessary;<BR>\n" );
document.write( "x+y=4 <BR>\n" );
document.write( "2x-y=-7<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "3x=-3<BR>\n" );
document.write( "x=-1<BR>\n" );
document.write( "Now substitute the -1 for x in one of the equations;<BR>\n" );
document.write( "-1+y=4<BR>\n" );
document.write( "y=5<BR>\n" );
document.write( "Since this has only one answer for x and y it is consistent and independent<BR>\n" );
document.write( "=============================================================================== <BR>\n" );
document.write( "y=-x+2<BR>\n" );
document.write( "3x+3y=6<BR>\n" );
document.write( "x+y=2<BR>\n" );
document.write( "-3x-3y=-6<BR>\n" );
document.write( "3x+3y=6<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "0=0<BR>\n" );
document.write( "This is the same line so it is infinitely many solutions<BR>\n" );
document.write( "===============================================================<BR>\n" );
document.write( "y=2/3x <BR>\n" );
document.write( "2x-y=-4<BR>\n" );
document.write( "-----------------\r<BR>\n" );
document.write( "\n" );
document.write( "-2/3)x+y=0<BR>\n" );
document.write( "    2x-y=-4<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29x=-4 ALIGN=MIDDLE  ALT=\"%284%2F3%29x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x=-3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29%28-3%29 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y=-2<BR>\n" );
document.write( "This has only one point, so it has only one solution<BR>\n" );
document.write( ":)<BR>\n" );
document.write( " </SPAN>\n" );
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