document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106473>Question 106473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello out there,I really need some help with some tough problems really bad,the first one is,Determine whether the system has one solution,no solution,or infinitely many solutions:y=2/3x and 2x-y=-4.The next one is,Determine whether the system has one solution,no solution,or infinitely many solutions:y=-x+2 and 3x+3y=6.The next one is,State whether the system is consistent and independent,consistent and dependent,or inconsistent:x+y=4 and 2x-y=-7.And the last one is,State whether the system is consistent and independent,consistent and dependent,or inconsistent:4x+2y=8 and 2x+y=1.Thanks to whoever can help me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77485 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77485\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> All you have to do to answer the above questions is get both equations in the slope-intercept form: y=mx+b<BR>\n" );
document.write( "m is the slope if m is different in each equation then the system is consistent and the system has an answer and the lines cross on the graph.<BR>\n" );
document.write( "If m is the same number (including sign) in both equations:<BR>\n" );
document.write( "I) If b is different in both equations then there is no answer and the graph shows parallel lines and the system is inconsistent.<BR>\n" );
document.write( "II) if b is equal in both equations then the equations are equal and consistent and has an infinate number of answers.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "y=2/3x<BR>\n" );
document.write( "2x-y=-4...-y=-2x-4...y=2x+4<BR>\n" );
document.write( "m=2/3 in the 1st equ. and 2x in the 2nd so they are consistent and there is a solution.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C%282%2F3%29x%2C2x%2B4%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C%282%2F3%29x%2C2x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "y=-x+2<BR>\n" );
document.write( "3x+3y=6...3y=-3x+6...y=-x+2<BR>\n" );
document.write( "These are the same equation. infinate number of answers.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x+y=4...y=-x+4<BR>\n" );
document.write( "2x-y=-7...-y=-2x-7...y=2x+7<BR>\n" );
document.write( "Has a solution<BR>\n" );
document.write( ".<BR>\n" );
document.write( "4x+2y=8...2y=-4x+8...y=-2x+4<BR>\n" );
document.write( "2x+y=1...y=-2x+1<BR>\n" );
document.write( "slopes are equal; b's are different.<BR>\n" );
document.write( "inconsistent, parallel lines<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-2x%2B4%2C-2x%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-2x%2B4%2C-2x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Not hard at all, once you know how to do them, huh.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Ed<BR>\n" );
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