document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=689901>Question 689901</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Do the equations x = 4y + 1 and x = 4y – 1 have the same solution? How might you explain your answer to someone who has not learned algebra? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #426083 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=426083\">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=x+=+4y+%2B+1 ALIGN=MIDDLE  ALT=\"x+=+4y+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4y+%96+1 ALIGN=MIDDLE  ALT=\"x+=+4y+%96+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if you assign a number to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve both equation 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;\" > you will need to get same value 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;\" > IF they have same solution\r<BR>\n" );
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document.write( "let's check it:\r<BR>\n" );
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document.write( "let's <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;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+4y+%2B+1 ALIGN=MIDDLE  ALT=\"0+=+4y+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...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=-1+=+4y+ ALIGN=MIDDLE  ALT=\"-1+=+4y+\"   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=highlight%28-1%2F4+=+y%29+ ALIGN=MIDDLE  ALT=\"highlight%28-1%2F4+=+y%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+4y+%96+1 ALIGN=MIDDLE  ALT=\"0+=+4y+%96+1\"   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=1+=+4y ALIGN=MIDDLE  ALT=\"1+=+4y\"   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=highlight%281%2F4+=+y%29 ALIGN=MIDDLE  ALT=\"highlight%281%2F4+=+y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight-1%2F4%3C%3E1%2F4++ ALIGN=MIDDLE  ALT=\"highlight-1%2F4%3C%3E1%2F4++\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the two equations do <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > have the same solution; it means these lines are parallel and do not intersect \r<BR>\n" );
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document.write( "check it on a graph\r<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+4y+%2B+1%2C+4y+-1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4y+%2B+1%2C+4y+-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you also can come to same conclusion this way:\r<BR>\n" );
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document.write( "first write both of them in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope-intercept ALIGN=MIDDLE  ALT=\"slope-intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" > form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4y+%2B+1 ALIGN=MIDDLE  ALT=\"x+=+4y+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=>..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1+=+4y ALIGN=MIDDLE  ALT=\"x-1+=+4y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.=>..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29x-1%2F4+=y ALIGN=MIDDLE  ALT=\"%281%2F4%29x-1%2F4+=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >. or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F4%29x-1%2F4+ ALIGN=MIDDLE  ALT=\"y=%281%2F4%29x-1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4y+-1 ALIGN=MIDDLE  ALT=\"x+=+4y+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=>..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1+=+4y ALIGN=MIDDLE  ALT=\"x%2B1+=+4y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.=>..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29x%2B1%2F4+=y ALIGN=MIDDLE  ALT=\"%281%2F4%29x%2B1%2F4+=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >. or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F4%29x%2B1%2F4+ ALIGN=MIDDLE  ALT=\"y=%281%2F4%29x%2B1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "as you can see both lines have same slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=1%2F4 ALIGN=MIDDLE  ALT=\"m=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and, by definition, the lines with same slope are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallel ALIGN=MIDDLE  ALT=\"parallel\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if the lines <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallel ALIGN=MIDDLE  ALT=\"parallel\"   DISABLED_style= \"max-width:90%; height:auto;\" >, they have no intersection point, and they have no same solution\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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