document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=424971>Question 424971</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i need your help in solving this equation: using comparion method\r<BR>\n" );
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document.write( "y=2x-3<BR>\n" );
document.write( "y=-1/2x+4\r<BR>\n" );
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document.write( "and this one using substitution method\r<BR>\n" );
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document.write( "x-2y=3<BR>\n" );
document.write( "2x-3y=y\r<BR>\n" );
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document.write( "thank you so much, ana<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296086 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=296086\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-3 ALIGN=MIDDLE  ALT=\"y=2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....1...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F2%29x%2B4 ALIGN=MIDDLE  ALT=\"y=-%281%2F2%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >....2\r<BR>\n" );
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document.write( "first multiply second equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > then add 1 and 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-3 ALIGN=MIDDLE  ALT=\"y=2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....1...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=4%28-1%2F2%29x%2B4%2A4 ALIGN=MIDDLE  ALT=\"4y=4%28-1%2F2%29x%2B4%2A4\"   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=y=2x-3 ALIGN=MIDDLE  ALT=\"y=2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....1...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=cross%284%292%28-1%2Fcross%282%29%29x%2B16 ALIGN=MIDDLE  ALT=\"4y=cross%284%292%28-1%2Fcross%282%29%29x%2B16\"   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=y=2x-3 ALIGN=MIDDLE  ALT=\"y=2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....1...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=-2x%2B16 ALIGN=MIDDLE  ALT=\"4y=-2x%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" >....2<BR>\n" );
document.write( "------------------------ now add them\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4y=2x%2B%28-2x%29-3%2B16 ALIGN=MIDDLE  ALT=\"y%2B4y=2x%2B%28-2x%29-3%2B16\"   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=5y=cross%282x%29%2Bcross%28%28-2x%29%29-3%2B16 ALIGN=MIDDLE  ALT=\"5y=cross%282x%29%2Bcross%28%28-2x%29%29-3%2B16\"   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=5y=13 ALIGN=MIDDLE  ALT=\"5y=13\"   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=13%2F5 ALIGN=MIDDLE  ALT=\"y=13%2F5\"   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=2.6 ALIGN=MIDDLE  ALT=\"y=2.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >....now find <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=y=2x-3 ALIGN=MIDDLE  ALT=\"y=2x-3\"   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=2.6%2B3=2x ALIGN=MIDDLE  ALT=\"2.6%2B3=2x\"   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=5.6=2x ALIGN=MIDDLE  ALT=\"5.6=2x\"   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=5.6%2F2=+x ALIGN=MIDDLE  ALT=\"5.6%2F2=+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=2.8=+x ALIGN=MIDDLE  ALT=\"2.8=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=-2x%2B16 ALIGN=MIDDLE  ALT=\"4y=-2x%2B16\"   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=4%2A2.6=-2%2A2.8%2B16 ALIGN=MIDDLE  ALT=\"4%2A2.6=-2%2A2.8%2B16\"   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=10.4+=+-5.6%2B16 ALIGN=MIDDLE  ALT=\"10.4+=+-5.6%2B16\"   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=10.4+=+10.4 ALIGN=MIDDLE  ALT=\"10.4+=+10.4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.\r<BR>\n" );
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document.write( "using substitution method\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=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++1%5Cx+%2B+-2%5Cy+=+3%2C%0D%0A++++2%5Cx+%2B+-4%5Cy+=+0+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++1%5Cx+%2B+-2%5Cy+=+3%2C%0D%0A++++2%5Cx+%2B+-4%5Cy+=+0+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving -2*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax+=+3+-+-2%2Ay ALIGN=MIDDLE  ALT=\"1%2Ax+=+3+-+-2%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F1+-+-2%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+3%2F1+-+-2%2Ay%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%283%2F1+-+-2%2Ay%2F1%29+%2B+-4%5Cy+=+0 ALIGN=MIDDLE  ALT=\"2%2A%283%2F1+-+-2%2Ay%2F1%29+%2B+-4%5Cy+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=6=0. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F1+-+-2%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+3%2F1+-+-2%2Ay%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=15.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=15%2C+y=6=0+%29 ALIGN=MIDDLE  ALT=\"system%28+x=15%2C+y=6=0+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  </TD></TR>\n" );
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