document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=214739>Question 214739</A>: <I><SPAN STYLE=\"word-break: break-all;\"> `6x+2y=8<BR>\n" );
document.write( "-3x+y=20<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 #162178 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=162178\">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=6x%2B2y=8 ALIGN=MIDDLE  ALT=\"6x%2B2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation A<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2By=20 ALIGN=MIDDLE  ALT=\"-3x%2By=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation B\r<BR>\n" );
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document.write( "Step 1.  Multiply Equation B by 2 and Add the two equations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%2B2y=40 ALIGN=MIDDLE  ALT=\"-6x%2B2y=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B2y=8 ALIGN=MIDDLE  ALT=\"6x%2B2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2.  This yields\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=48 ALIGN=MIDDLE  ALT=\"4y=48\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=12 ALIGN=MIDDLE  ALT=\"y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3.  Substitue y=12 into equation A or B.  Here's for Equation A\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B2%2A12=8 ALIGN=MIDDLE  ALT=\"6x%2B2%2A12=8\"   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=6x=-16 ALIGN=MIDDLE  ALT=\"6x=-16\"   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=x=-16%2F6=-8%2F3 ALIGN=MIDDLE  ALT=\"x=-16%2F6=-8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 4.  ANSWER:  The solution is x=-8/3 and  y=12.\r<BR>\n" );
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document.write( "As a check here's the solution using 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++++6%5Cx+%2B+2%5Cy+=+8%2C%0D%0A++++-3%5Cx+%2B+1%5Cy+=+20+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++6%5Cx+%2B+2%5Cy+=+8%2C%0D%0A++++-3%5Cx+%2B+1%5Cy+=+20+%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=6%2Ax+=+8+-+2%2Ay ALIGN=MIDDLE  ALT=\"6%2Ax+=+8+-+2%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8%2F6+-+2%2Ay%2F6 ALIGN=MIDDLE  ALT=\"x+=+8%2F6+-+2%2Ay%2F6\"   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=-3%2A%288%2F6+-+2%2Ay%2F6%29+%2B+1%5Cy+=+20 ALIGN=MIDDLE  ALT=\"-3%2A%288%2F6+-+2%2Ay%2F6%29+%2B+1%5Cy+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=12. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8%2F6+-+2%2Ay%2F6 ALIGN=MIDDLE  ALT=\"x+=+8%2F6+-+2%2Ay%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=-2.66666666666667.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=-2.66666666666667%2C+y=12+%29 ALIGN=MIDDLE  ALT=\"system%28+x=-2.66666666666667%2C+y=12+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "The results are the same as before.\r<BR>\n" );
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document.write( "I hope the above steps were helpful. \r<BR>\n" );
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document.write( "For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "And good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J<BR>\n" );
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