document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=914249>Question 914249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am very desperate here and have no clue were to turn.  I am a single mother of 3 45 yrs old whom went back to college and now feel really stupid.  I am forced to take this course as part of my goals to obtain my degree. Were doing solving systems of linear equations by substitution and i have no clue how to do it i have worked countless hours on this and many other chapters and just can't get it and i have to complete three chapters by the 21st for my midterm grade if not i'm going to just have to crush my dreams by dropping out of college and looking like a failure to my kids.  the question is:  Solve the following system of linear equations by substitution:<BR>\n" );
document.write( "{-2x+y=24<BR>\n" );
document.write( "{5y  =10x+120<BR>\n" );
document.write( "These are all in one bracket not two i have no clue how to make it just one bracket.  Then under it say's please select whether the given system of linear equations is consistent, inconsistent, or dependent.  if the system is consistent, please enter the solution. <BR>\n" );
document.write( "Thank you so much for helping me and others out there.<BR>\n" );
document.write( "Rebecca </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #554951 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=554951\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2By=24 ALIGN=MIDDLE  ALT=\"-2x%2By=24\"   DISABLED_style= \"max-width:90%; height:auto;\" > for y. So isolate y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2By=24 ALIGN=MIDDLE  ALT=\"-2x%2By=24\"   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%2B24 ALIGN=MIDDLE  ALT=\"y+=+2x%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > add 2x to both sides\r<BR>\n" );
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document.write( "Now that y is fully isolated, we plug this into the second equation. This is where the term \"substitution\" comes from. We substitute y for 2x+24\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+=10x%2B120 ALIGN=MIDDLE  ALT=\"5y+=10x%2B120\"   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=5%28y%29+=10x%2B120 ALIGN=MIDDLE  ALT=\"5%28y%29+=10x%2B120\"   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=5%282x%2B24%29+=10x%2B120 ALIGN=MIDDLE  ALT=\"5%282x%2B24%29+=10x%2B120\"   DISABLED_style= \"max-width:90%; height:auto;\" > replace EVERY copy of y with 2x+24\r<BR>\n" );
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document.write( "Now we have eliminated every copy of y. We can now solve for x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%282x%2B24%29=10x%2B120 ALIGN=MIDDLE  ALT=\"5%282x%2B24%29=10x%2B120\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2B120=10x%2B120 ALIGN=MIDDLE  ALT=\"10x%2B120=10x%2B120\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x=10x%2B120-120 ALIGN=MIDDLE  ALT=\"10x=10x%2B120-120\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120 ALIGN=MIDDLE  ALT=\"120\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x-10x=120-120 ALIGN=MIDDLE  ALT=\"10x-10x=120-120\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x ALIGN=MIDDLE  ALT=\"10x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x=120-120 ALIGN=MIDDLE  ALT=\"0x=120-120\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x=0 ALIGN=MIDDLE  ALT=\"0x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\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;\" > Simplify.\r<BR>\n" );
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document.write( "Since this equation is <font size=4><b>ALWAYS</b></font> true for any x value, this means x can equal any number. So there are an infinite number of solutions.\r<BR>\n" );
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document.write( "So there are <font size=5 color=\"red\">infinitely many solutions</font> for this system. \r<BR>\n" );
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document.write( "This means that the system is <font size=5 color=\"red\">dependent</font> (one equation \"depends\" on the other; I like to think of it as one line leaning on the other)\r<BR>\n" );
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document.write( "Graphically, these 2 equations form the same line. One line lies perfectly on top of the other. This results in infinitely many intersections (recall that an intersection visually corresponds to a solution).\r<BR>\n" );
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document.write( "Let me know if you need more help or if you need me to explain a step in more detail.<BR>\n" );
document.write( "Feel free to email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a><BR>\n" );
document.write( "or you can visit my website here: <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">http://www.freewebs.com/jimthompson5910/home.html</a>\r<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Jim  </SPAN>\n" );
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