document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=695848>Question 695848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I've been having trouble with Linear equations. Can you help me how to solve them step by step? Thanks\r<BR>\n" );
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document.write( "y<x^2+1<BR>\n" );
document.write( "y>-x^2+1\r<BR>\n" );
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document.write( "p.s: I need to Graph it too. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #428659 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=428659\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Something went wrong (got lost in translation) while you were entering the problem. Maybe you had some typos.<BR>\n" );
document.write( "Or maybe not everything you typed is shown the way you meant because of the way characters are coded by computers.<BR>\n" );
document.write( "Linear equations (in their most simplified form) do not have exponents on the variables, and I see exponents, so maybe you meant non-linear.<BR>\n" );
document.write( "Equations involve equal signs, but I see a > sign instead, which would make it an inequality instead of an equation.<BR>\n" );
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document.write( "Maybe you meant you have to solve, by graphing, the system of non-linear inequalities<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y%3Cx%5E2%2B1%2Cy%3E-x%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"system%28y%3Cx%5E2%2B1%2Cy%3E-x%5E2%2B1%29\"   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=x%5E2%2B1 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a non-linear equation. It can also be called a non-linear function.<BR>\n" );
document.write( "Because the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is squared it can also be called a quadratic function.<BR>\n" );
document.write( "The graph for the quadratic function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B1 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C180%2C-5%2C5%2C-5%2C25%2Cx%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C180%2C-5%2C5%2C-5%2C25%2Cx%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C180%2C-5%2C5%2C-25%2C5%2Cy=6%2C-x%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C180%2C-5%2C5%2C-25%2C5%2Cy=6%2C-x%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the graph of quadratic function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B1 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Graphing both together, you would have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C5%2C-25%2C25%2Cx%5E2%2B1%2C-x%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C5%2C-25%2C25%2Cx%5E2%2B1%2C-x%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The graphs touch at the point where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "To graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3Cx%5E2%2B1 ALIGN=MIDDLE  ALT=\"y%3Cx%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > you would just<BR>\n" );
document.write( "graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B1 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a dotted line (to show that those points are not part of the solution),<BR>\n" );
document.write( "and then you would color or shade the points (below the curve) that have smaller <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > values, to get something like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C180%2C-5%2C5%2C-5%2C25%2Cy%3Cx%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C180%2C-5%2C5%2C-5%2C25%2Cy%3Cx%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E-x%5E2%2B1 ALIGN=MIDDLE  ALT=\"y%3E-x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you would graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%5E2%2B1 ALIGN=MIDDLE  ALT=\"y=-x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a dotted line,<BR>\n" );
document.write( "and then you would color or shade the points (above the curve) that have larger <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > values, to get something like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C180%2C-5%2C5%2C-25%2C5%2Cy%3E-x%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C180%2C-5%2C5%2C-25%2C5%2Cy%3E-x%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y%3Cx%5E2%2B1%2Cy%3E-x%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"system%28y%3Cx%5E2%2B1%2Cy%3E-x%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > you would just graph both curves as dotted lines<BR>\n" );
document.write( "(to show that those points are not part of the solution),<BR>\n" );
document.write( "and then you would color or shade the points in between,<BR>\n" );
document.write( "the ones that are part of the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3Cx%5E2%2B1 ALIGN=MIDDLE  ALT=\"y%3Cx%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and also are part of the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E-x%5E2%2B1 ALIGN=MIDDLE  ALT=\"y%3E-x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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