document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=487417>Question 487417</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can someone please help me? <BR>\n" );
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document.write( "solve each system by the substitution method.\r<BR>\n" );
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document.write( "10. 4x+2y=-8<BR>\n" );
document.write( "    2x+y=-4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #333048 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=333048\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B2y=-8 ALIGN=MIDDLE  ALT=\"4x%2B2y=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By=-4 ALIGN=MIDDLE  ALT=\"2x%2By=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By=-4 ALIGN=MIDDLE  ALT=\"2x%2By=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........2...solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x-4 ALIGN=MIDDLE  ALT=\"y=-2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >...substitute in 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B2%28-2x-4%29=-8 ALIGN=MIDDLE  ALT=\"4x%2B2%28-2x-4%29=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......1..solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-4x-8=-8 ALIGN=MIDDLE  ALT=\"4x-4x-8=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-4x=-8%2B8 ALIGN=MIDDLE  ALT=\"4x-4x=-8%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......there are an infinite number of solutions and the system is dependent\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_by_graphing.solver>Solve the System of Equations by Graphing</A></TD></TR>\n" );
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document.write( "  Start with the given system of equations:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By=-4 ALIGN=MIDDLE  ALT=\"2x%2By=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  In order to graph these equations, we need to solve for y for each equation.<BR>\n" );
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document.write( "  So let's solve for y on the first equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B2y=-8 ALIGN=MIDDLE  ALT=\"4x%2B2y=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=-8-4x ALIGN=MIDDLE  ALT=\"2y=-8-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+x ALIGN=MIDDLE  ALT=\"4+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=-4x-8 ALIGN=MIDDLE  ALT=\"2y=-4x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-4x-8%29%2F%282%29 ALIGN=MIDDLE  ALT=\"y=%28-4x-8%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-4%2F2%29x%2B%28-8%29%2F%282%29 ALIGN=MIDDLE  ALT=\"y=%28-4%2F2%29x%2B%28-8%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x-4 ALIGN=MIDDLE  ALT=\"y=-2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
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document.write( "  Now lets graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x-4 ALIGN=MIDDLE  ALT=\"y=-2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: if you need help with graphing, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver</a>)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x-4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x-4 ALIGN=MIDDLE  ALT=\"y=-2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So let's solve for y on the second equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By=-4 ALIGN=MIDDLE  ALT=\"2x%2By=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1y=-4-2x ALIGN=MIDDLE  ALT=\"1y=-4-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+x ALIGN=MIDDLE  ALT=\"2+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1y=-2x-4 ALIGN=MIDDLE  ALT=\"1y=-2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2x-4%29%2F%281%29 ALIGN=MIDDLE  ALT=\"y=%28-2x-4%29%2F%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2%2F1%29x%2B%28-4%29%2F%281%29 ALIGN=MIDDLE  ALT=\"y=%28-2%2F1%29x%2B%28-4%29%2F%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x-4 ALIGN=MIDDLE  ALT=\"y=-2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
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document.write( "  Now lets add the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x-4 ALIGN=MIDDLE  ALT=\"y=-2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to our first plot to get:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x-4%2C-2x-4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x-4%2C-2x-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x-4 ALIGN=MIDDLE  ALT=\"y=-2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >(red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x-4 ALIGN=MIDDLE  ALT=\"y=-2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >(green)<BR>\n" );
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document.write( "  From the graph, we can see that the two lines are identical (one lies perfectly on top of the other) and intersect at all points of both lines. So there are an infinite number of solutions and the system is dependent.</TD></TR>\n" );
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