document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177973>Question 177973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each system by the addition method. determine whether he equations are independent, dependent, or inconsistent.\r<BR>\n" );
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document.write( "x-y=3<BR>\n" );
document.write( "-6x+6y=17\r<BR>\n" );
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document.write( "Thanks!!<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 #132939 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=132939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\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=solving_linear_system_by_elimination.solver>Solving a System of Linear Equations by Elimination/Addition</A></TD></TR>\n" );
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document.write( "  Lets start with the given system of linear equations<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax-1%2Ay=3 ALIGN=MIDDLE  ALT=\"1%2Ax-1%2Ay=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2Ax%2B6%2Ay=17 ALIGN=MIDDLE  ALT=\"-6%2Ax%2B6%2Ay=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).<BR>\n" );
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document.write( "  So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.<BR>\n" );
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document.write( "  So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 1 and -6 to some equal number, we could try to get them to the LCM.<BR>\n" );
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document.write( "  Since the LCM of 1 and -6 is -6, we need to multiply both sides of the top equation by -6 and multiply both sides of the bottom equation by -1 like this:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2A%281%2Ax-1%2Ay%29=%283%29%2A-6 ALIGN=MIDDLE  ALT=\"-6%2A%281%2Ax-1%2Ay%29=%283%29%2A-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the top equation (both sides) by -6<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2A%28-6%2Ax%2B6%2Ay%29=%2817%29%2A-1 ALIGN=MIDDLE  ALT=\"-1%2A%28-6%2Ax%2B6%2Ay%29=%2817%29%2A-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the bottom equation (both sides) by -1<BR>\n" );
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document.write( "  So after multiplying we get this:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2Ax%2B6%2Ay=-18 ALIGN=MIDDLE  ALT=\"-6%2Ax%2B6%2Ay=-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Ax-6%2Ay=-17 ALIGN=MIDDLE  ALT=\"6%2Ax-6%2Ay=-17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Notice how -6 and 6 and -18 and -6 add to zero (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2B6=0 ALIGN=MIDDLE  ALT=\"-6%2B6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2B-6=0 ALIGN=MIDDLE  ALT=\"6%2B-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  However -18 and -17 add to -35 (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18%2B-17=-35 ALIGN=MIDDLE  ALT=\"-18%2B-17=-35\"   DISABLED_style= \"max-width:90%; height:auto;\" >);<BR>\n" );
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document.write( "  So we're left with <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-35 ALIGN=MIDDLE  ALT=\"0=-35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  which means no value of x or y value will satisfy the system of equations. So there are no solutions<BR>\n" );
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document.write( "  So this system is <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/coordinate/lessons/Types-of-systems-inconsistent-dependent-independent.lesson>inconsistent</a></TD></TR>\n" );
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