document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27066>Question 27066</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2y+x=4<BR>\n" );
document.write( "4y=x-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #14725 by </B><A HREF=/tutors/aboutme.mpl?userid=mbarugel><B>mbarugel(146)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mbarugel><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=14725\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The best way to solve these 2x2 linear systems is to first write them in the following form:\r<BR>\n" );
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document.write( "Ax + By = C<BR>\n" );
document.write( "Dx + Ey = F\r<BR>\n" );
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document.write( "And then use the general formula (which you'll find below) to find the solution. We have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2Bx=4 ALIGN=MIDDLE  ALT=\"2y%2Bx=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x+%2B+2y+=+4 ALIGN=MIDDLE  ALT=\"1x+%2B+2y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We also have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y+=+x+-+1 ALIGN=MIDDLE  ALT=\"4y+=+x+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which is the same as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x+-+4y+=+1 ALIGN=MIDDLE  ALT=\"1x+-+4y+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we have the system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x+%2B+2y+=+4 ALIGN=MIDDLE  ALT=\"1x+%2B+2y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x+-+4y+=+1 ALIGN=MIDDLE  ALT=\"1x+-+4y+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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.solver>Linear System solver (using determinant)</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+=+4%2C%0D%0A++++1%5Cx+%2B+-4%5Cy+=+1+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++1%5Cx+%2B+2%5Cy+=+4%2C%0D%0A++++1%5Cx+%2B+-4%5Cy+=+1+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Any system of equations:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++a%5B11%5D%2Ax+%2B+a%5B12%5D%2Ay+=+b%5B1%5D%2C%0D%0A++++a%5B21%5D%2Ax+%2B+a%5B22%5D%2Ay+=+b%5B2%5D%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  has solution<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++x+=+%28b%5B1%5D%2Aa%5B22%5D+-+b%5B2%5D%2Aa%5B12%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%2C%0D%0A++++y+=+%28a%5B11%5D%2Ab%5B2%5D+-+a%5B21%5D%2Ab%5B1%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  or<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++++x+=+%284%2A-4+-+1%2A2%29%2F%281%2A-4-1%2A2%29+=+3%2C%0D%0A++++++y+=+%281%2A1+-+1%2A4%29%2F%281%2A-4-1%2A2%29+=+0.5%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  (x=3, y=0.5}<BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( " </SPAN>\n" );
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