document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124954>Question 124954</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am confused can someone help? I need to solve each system by the substitution method and determine if they are independent, dependent, or inconsistent.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=x%2B6 ALIGN=MIDDLE  ALT=\"2y=x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > first line<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B2y=-2 ALIGN=MIDDLE  ALT=\"-3x%2B2y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91609 by </B><A HREF=/tutors/aboutme.mpl?userid=chitra><B>chitra(359)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chitra><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=91609\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The given equations are: \r<BR>\n" );
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document.write( "2y = x + 6  ---------------(1) \r<BR>\n" );
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document.write( "-3x + 2y = -2 --------------(2) \r<BR>\n" );
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document.write( "Substituting (1) in (2) we get: \r<BR>\n" );
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document.write( "-3x + x + 6 = - 2\r<BR>\n" );
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document.write( "-2x = -2 - 6 \r<BR>\n" );
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document.write( "-2x = -8 \r<BR>\n" );
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document.write( "x = 4 \r<BR>\n" );
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document.write( "By back substitution we get the \"y\" value: \r<BR>\n" );
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document.write( "2y = 10 \r<BR>\n" );
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document.write( "==> y = 5 \r<BR>\n" );
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document.write( "So we observe that the line intersects at (4,5) for both the graphs. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-20%2C+20%2C+-20%2C+20%2C+x%2F2+%2B+3%2C+1.5x+-1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-20%2C+20%2C+-20%2C+20%2C+x%2F2+%2B+3%2C+1.5x+-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Hence the given system of equations are Consistent & Dependent\r<BR>\n" );
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document.write( "Thus the solution. \r<BR>\n" );
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document.write( "Here are the notes that will help you determine the category under which they fall.\r<BR>\n" );
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document.write( "If the two equations describe the same line, and thus lines that intersect an infinite number of times, the system is dependent and consistent.\r<BR>\n" );
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document.write( "If the two equations describe lines that intersect once, the system is independent and consistent.\r<BR>\n" );
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document.write( "If the two equations describe parallel lines, and thus lines that do not intersect, the system is independent and inconsistent.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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