document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139270>Question 139270</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by the elimination method.<BR>\n" );
document.write( "3x+4y=3<BR>\n" );
document.write( "6x+8y=6<BR>\n" );
document.write( "What is the solution of the system. Help me please. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101543 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=101543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The method requires finding a constant that you can multiply one of the equations by so that one of the coefficients on one of the variables becomes the additive inverse of the coefficient on the same variable in the other equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y=3 ALIGN=MIDDLE  ALT=\"3x%2B4y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B8y=6 ALIGN=MIDDLE  ALT=\"6x%2B8y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we have 3 and 6 as coefficients on the x terms, if we multiply the first equation by -2, that will give us -6 on the x in the first equation and 6 on the x in the second equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x-8y=-6 ALIGN=MIDDLE  ALT=\"-6x-8y=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B8y=6 ALIGN=MIDDLE  ALT=\"6x%2B8y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now just add the equations, term by term:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B0y=0 ALIGN=MIDDLE  ALT=\"0x%2B0y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And the result is a special case situation.  We have achieved an identity result, namely <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This means that ALL ordered pairs in the solution set of the first equation are also in the solution set of the second equation.  In other words, they are exactly the same line.  There is no single solution to this system, so you can say that the system is consistent (the two equations have at least one element of their solution sets in common) and dependent (all elements of one solution set are elements of the other solution set).\r<BR>\n" );
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