document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=218305>Question 218305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone explain the Gauss-Jordan elimination method to solve this system of linear equations?<BR>\n" );
document.write( "2x+ y= 5<BR>\n" );
document.write( "4x+ 3y= 11\r<BR>\n" );
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document.write( "Is the solution (2,1) or am I wrong?  thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #164394 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=164394\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Can someone explain the Gauss-Jordan elimination method to solve this system of linear equations?\r<BR>\n" );
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document.write( "2x+ y= 5  Equation A<BR>\n" );
document.write( "4x+ 3y= 11  Equation B\r<BR>\n" );
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document.write( "Is the solution (2,1) or am I wrong?  thank you.\r<BR>\n" );
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document.write( "Step 1  Check (2,1) by substituting into Equations A and B where x=2 and y=1.\r<BR>\n" );
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document.write( "2*2+1= 5  or 5=5 which satisfies Equation A.\r<BR>\n" );
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document.write( "4*2+3*1=8+3=11 of 11=11  which satisfies Equation B.\r<BR>\n" );
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document.write( "Step 2.  The elimination method in this example means when you multiply either Equation A or B by a factor such that when you add or subtract these two equations, one of the variables x or y will be eliminated.  When you eliminate a variable, then you have an equation with one variable in this case.\r<BR>\n" );
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document.write( "Step 3.  As an example, take Equation A and multiply by -2.  This yields\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x-2y=-10 ALIGN=MIDDLE  ALT=\"-4x-2y=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation A1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B3y=11 ALIGN=MIDDLE  ALT=\"4x%2B3y=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Equation B\r<BR>\n" );
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document.write( "Now when you add these two equations A1 and B, this will yield\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%2B4x-2y%2B3y=-10%2B11 ALIGN=MIDDLE  ALT=\"-4x%2B4x-2y%2B3y=-10%2B11\"   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=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  This leaves a single equation with y=1.\r<BR>\n" );
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document.write( "Step 4.  As another example take Equation A and multiply by -3.  This yields\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x-3y=-15 ALIGN=MIDDLE  ALT=\"-6x-3y=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Equation A2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B+3y=+11 ALIGN=MIDDLE  ALT=\"4x%2B+3y=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation B\r<BR>\n" );
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document.write( "Adding these two Equations A2 and B yields\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%2B4x-3y%2B3y=-15%2B11 ALIGN=MIDDLE  ALT=\"-6x%2B4x-3y%2B3y=-15%2B11\"   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=-2x=-4 ALIGN=MIDDLE  ALT=\"-2x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >   where we eliminated the y-terms and have a single variable in the equation.\r<BR>\n" );
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document.write( "Now divide -2 to both sides of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the solution is x=2 and  y=1 or at point (2,1) as a solution given earlier in the problem.\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 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 </SPAN>\n" );
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