document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=218697>Question 218697</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the system using the linear combination method<BR>\n" );
document.write( "4x+2y=2<BR>\n" );
document.write( "5x-2y=-11 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #164667 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=164667\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the system using the linear combination method\r<BR>\n" );
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document.write( "4x+2y=2  Equation A<BR>\n" );
document.write( "5x-2y=-11  Equation B\r<BR>\n" );
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document.write( "This is the elimination method (don't know if that's what your teacher means by the linear combination method.  I think this is ok because you are just taking a linear combination of Equations A and B to yield another equation).\r<BR>\n" );
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document.write( "Add the two equations A and B to ge 9x=-9 or x=-1.  Substituting x=-1 into Equation A yields -4+2y=2 or 2y=6 and  y=3.  \r<BR>\n" );
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document.write( "So solution is (-1,3).\r<BR>\n" );
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document.write( "The following solves using the Substituion method with the same results.\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++++4%5Cx+%2B+2%5Cy+=+2%2C%0D%0A++++5%5Cx+%2B+-2%5Cy+=+-11+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++4%5Cx+%2B+2%5Cy+=+2%2C%0D%0A++++5%5Cx+%2B+-2%5Cy+=+-11+%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=4%2Ax+=+2+-+2%2Ay ALIGN=MIDDLE  ALT=\"4%2Ax+=+2+-+2%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2F4+-+2%2Ay%2F4 ALIGN=MIDDLE  ALT=\"x+=+2%2F4+-+2%2Ay%2F4\"   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=5%2A%282%2F4+-+2%2Ay%2F4%29+%2B+-2%5Cy+=+-11 ALIGN=MIDDLE  ALT=\"5%2A%282%2F4+-+2%2Ay%2F4%29+%2B+-2%5Cy+=+-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=3. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2F4+-+2%2Ay%2F4 ALIGN=MIDDLE  ALT=\"x+=+2%2F4+-+2%2Ay%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=-1.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=-1%2C+y=3+%29 ALIGN=MIDDLE  ALT=\"system%28+x=-1%2C+y=3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<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 in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and 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\r<BR>\n" );
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document.write( "http://www.FreedomUniversity.TV<BR>\n" );
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