document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73737>Question 73737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Y= -1/3X+1<BR>\n" );
document.write( "Y= 1/3X-3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52740 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52740\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=+-%281%2F3%29X%2B1 ALIGN=MIDDLE  ALT=\"Y=+-%281%2F3%29X%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=+%281%2F3%29X-3 ALIGN=MIDDLE  ALT=\"Y=+%281%2F3%29X-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Find the common solution.<BR>\n" );
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document.write( "Notice that the left sides of both these equations are equal (both of them are Y) so, the<BR>\n" );
document.write( "right sides must be equal also. Set them equal:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F3%29X%2B1=%281%2F3%29X-3 ALIGN=MIDDLE  ALT=\"-%281%2F3%29X%2B1=%281%2F3%29X-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can avoid messing with fractions if you multiply both sides (all the terms) of this equation <BR>\n" );
document.write( "by the common denominator 3.  When you do the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-X+%2B+3+=+X+-+9 ALIGN=MIDDLE  ALT=\"-X+%2B+3+=+X+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Remove the X from the right side by subtracting X from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2X+%2B+3+=+-+9 ALIGN=MIDDLE  ALT=\"-2X+%2B+3+=+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Eliminate +3 from the left side by subtracting +3 from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2X+=+-+12 ALIGN=MIDDLE  ALT=\"+-2X+=+-+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for X by dividing both sides by -2 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+-12%2F-2+=+6 ALIGN=MIDDLE  ALT=\"X+=+-12%2F-2+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now that we know that X equals 6, we can solve for y by returning to either of the original<BR>\n" );
document.write( "equations and substituting 6 for X.<BR>\n" );
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document.write( "For example, let's return to the second (or bottom) of these equations to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=+%281%2F3%29X-3 ALIGN=MIDDLE  ALT=\"Y=+%281%2F3%29X-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and by substituting 6 for X it becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=+%281%2F3%29%2A6-3+=+2+-+3+=+-1 ALIGN=MIDDLE  ALT=\"Y=+%281%2F3%29%2A6-3+=+2+-+3+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That's all there is to it. The common solution is X = 6 and Y = -1.<BR>\n" );
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document.write( "Hope that this helps you to understand the process of solving simultaneously for two linear<BR>\n" );
document.write( "equations.\r<BR>\n" );
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