document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1130654>Question 1130654</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use elimination to solve the system. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y.)\r<BR>\n" );
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document.write( "x &#8722; y = 9<BR>\n" );
document.write( "1/3 x = 1/3 y + 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747292 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=747292\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-y+=+9 ALIGN=MIDDLE  ALT=\"x+-y+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29+x+=+%281%2F3%29+y+%2B+3 ALIGN=MIDDLE  ALT=\"%281%2F3%29+x+=+%281%2F3%29+y+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-y+=+9 ALIGN=MIDDLE  ALT=\"x+-y+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29+x+-%281%2F3%29+y=+3 ALIGN=MIDDLE  ALT=\"%281%2F3%29+x+-%281%2F3%29+y=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=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( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2Ax%2B%28-1%2F3%29%2Ay=3 ALIGN=MIDDLE  ALT=\"%281%2F3%29%2Ax%2B%28-1%2F3%29%2Ay=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28%281%2F3%29%2Ax%2B%28-1%2F3%29%2Ay%29=%283%29%2A%283%29 ALIGN=MIDDLE  ALT=\"3%28%281%2F3%29%2Ax%2B%28-1%2F3%29%2Ay%29=%283%29%2A%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD 3<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax%2B-1%2Ay=9 ALIGN=MIDDLE  ALT=\"1%2Ax%2B-1%2Ay=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and simplify<BR>\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=9 ALIGN=MIDDLE  ALT=\"1%2Ax-1%2Ay=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax-1%2Ay=9 ALIGN=MIDDLE  ALT=\"1%2Ax-1%2Ay=9\"   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 1 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 1 is 1, we need to multiply both sides of the top equation by 1 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=1%2A%281%2Ax-1%2Ay%29=%289%29%2A1 ALIGN=MIDDLE  ALT=\"1%2A%281%2Ax-1%2Ay%29=%289%29%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the top equation (both sides) by 1<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2A%281%2Ax-1%2Ay%29=%289%29%2A-1 ALIGN=MIDDLE  ALT=\"-1%2A%281%2Ax-1%2Ay%29=%289%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=1%2Ax-1%2Ay=9 ALIGN=MIDDLE  ALT=\"1%2Ax-1%2Ay=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Ax%2B1%2Ay=-9 ALIGN=MIDDLE  ALT=\"-1%2Ax%2B1%2Ay=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Notice how 1 and -1 add to zero, -1 and 1 add to zero, 9 and -9 and to zero (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B-1=0 ALIGN=MIDDLE  ALT=\"1%2B-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2B1=0 ALIGN=MIDDLE  ALT=\"-1%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2B-9=0 ALIGN=MIDDLE  ALT=\"9%2B-9=0\"   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=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  which means any x or y value will satisfy the system of equations. So there are an infinite number of 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>dependent</a></TD></TR>\n" );
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