document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27654>Question 27654</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve by using the best method for each system.<BR>\n" );
document.write( "3x-3y=18 and <BR>\n" );
document.write( "x+y=3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15028 by </B><A HREF=/tutors/aboutme.mpl?userid=askmemath><B>askmemath(368)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=askmemath><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=15028\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3x-3y=18  <BR>\n" );
document.write( "x+y=3\r<BR>\n" );
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document.write( "Multiplying the 2nd equation with 3<BR>\n" );
document.write( "3x+3y = 9<BR>\n" );
document.write( "Now, adding both<BR>\n" );
document.write( "6x = 27<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+27%2F6 ALIGN=MIDDLE  ALT=\"X+=+27%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "X = 4.5<BR>\n" );
document.write( "Putting this  value back into any equation we get Y = -1.5\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++++3%5Cx+%2B+-3%5Cy+=+18%2C%0D%0A++++1%5Cx+%2B+1%5Cy+=+3+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++3%5Cx+%2B+-3%5Cy+=+18%2C%0D%0A++++1%5Cx+%2B+1%5Cy+=+3+%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+=+%2818%2A1+-+3%2A-3%29%2F%283%2A1-1%2A-3%29+=+4.5%2C%0D%0A++++++y+=+%283%2A3+-+1%2A18%29%2F%283%2A1-1%2A-3%29+=+-1.5%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  (x=4.5, y=-1.5}<BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<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++++3%5Cx+%2B+-3%5Cy+=+18%2C%0D%0A++++1%5Cx+%2B+1%5Cy+=+3+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++3%5Cx+%2B+-3%5Cy+=+18%2C%0D%0A++++1%5Cx+%2B+1%5Cy+=+3+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving -3*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax+=+18+-+-3%2Ay ALIGN=MIDDLE  ALT=\"3%2Ax+=+18+-+-3%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+18%2F3+-+-3%2Ay%2F3 ALIGN=MIDDLE  ALT=\"x+=+18%2F3+-+-3%2Ay%2F3\"   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=1%2A%2818%2F3+-+-3%2Ay%2F3%29+%2B+1%5Cy+=+3 ALIGN=MIDDLE  ALT=\"1%2A%2818%2F3+-+-3%2Ay%2F3%29+%2B+1%5Cy+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=-1.5. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+18%2F3+-+-3%2Ay%2F3 ALIGN=MIDDLE  ALT=\"x+=+18%2F3+-+-3%2Ay%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=4.5.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=4.5%2C+y=-1.5+%29 ALIGN=MIDDLE  ALT=\"system%28+x=4.5%2C+y=-1.5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );