document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123099>Question 123099</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with the following: \r<BR>\n" );
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document.write( "Solve by substitution x + y = 12<BR>\n" );
document.write( "                      y = 2x\r<BR>\n" );
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document.write( "Solve by addition 5x - 3y = 13<BR>\n" );
document.write( "                  4x - 3y = 11\r<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 #90347 by </B><A HREF=/tutors/aboutme.mpl?userid=johnnico6426><B>johnnico6426(16)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=johnnico6426><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=90347\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Substitution:\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+1%5Cy+=+12%2C%0D%0A++++-2%5Cx+%2B+1%5Cy+=+0+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+12%2C%0D%0A++++-2%5Cx+%2B+1%5Cy+=+0+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 1*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax+=+12+-+1%2Ay ALIGN=MIDDLE  ALT=\"1%2Ax+=+12+-+1%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12%2F1+-+1%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+12%2F1+-+1%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%2812%2F1+-+1%2Ay%2F1%29+%2B+1%5Cy+=+0 ALIGN=MIDDLE  ALT=\"-2%2A%2812%2F1+-+1%2Ay%2F1%29+%2B+1%5Cy+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=8. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12%2F1+-+1%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+12%2F1+-+1%2Ay%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=4.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=4%2C+y=8+%29 ALIGN=MIDDLE  ALT=\"system%28+x=4%2C+y=8+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Addition:\r<BR>\n" );
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document.write( "5x - 3y = 13<BR>\n" );
document.write( "4x - 3y = 11\r<BR>\n" );
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document.write( "Multiply the top part with -4 and the buttom with 5\r<BR>\n" );
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document.write( "-20x + 12y = -52<BR>\n" );
document.write( " 20x - 15y =  55\r<BR>\n" );
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document.write( "You add them down\r<BR>\n" );
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document.write( "-3y = 3\r<BR>\n" );
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document.write( "Solve for y.\r<BR>\n" );
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document.write( "y=-1\r<BR>\n" );
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document.write( "Subsitute y=3 for the y in either the first and second equation. Solve for x. You should get x=2. The solution should be (2, -1)\r<BR>\n" );
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