document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123337>Question 123337</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x-3y=0<BR>\n" );
document.write( "xy=27 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90525 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=90525\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the two equations:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+3y+=+0 ALIGN=MIDDLE  ALT=\"x+-+3y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay+=+27 ALIGN=MIDDLE  ALT=\"x%2Ay+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let's use substitution as a start for solving for x and y. Go to the second equation and<BR>\n" );
document.write( "solve for y by dividing both sides of the equation by x to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+27%2Fx ALIGN=MIDDLE  ALT=\"y+=+27%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you can go to the first equation and replace y by its equal which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%2Fx ALIGN=MIDDLE  ALT=\"27%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >. When<BR>\n" );
document.write( "you make that replacement in the first equation it becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+3%2A%2827%2Fx%29+=+0 ALIGN=MIDDLE  ALT=\"x+-+3%2A%2827%2Fx%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply the -3 times the numerator 27 and this equation then is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-81%2Fx+=+0 ALIGN=MIDDLE  ALT=\"x+-81%2Fx+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can next get rid of the denominator of x by multiplying both sides of the equation (all terms)<BR>\n" );
document.write( "by x to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+81+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+81+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the -81 on the left side by adding +81 to both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+81 ALIGN=MIDDLE  ALT=\"x%5E2+=+81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Take the square root of both sides and you have two answers:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+9 ALIGN=MIDDLE  ALT=\"x+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-9 ALIGN=MIDDLE  ALT=\"x+=+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So there are also two possible answers for y. Recall that we had <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+27%2Fx ALIGN=MIDDLE  ALT=\"y+=+27%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This means that<BR>\n" );
document.write( "when x = +9 the corresponding value of y is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+27%2F9+=+3 ALIGN=MIDDLE  ALT=\"y+=+27%2F9+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "And when x = -9 the corresponding value of y is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+27%2F-9+=+-3 ALIGN=MIDDLE  ALT=\"y+=+27%2F-9+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the two possible answers to this problem are the pair x = 9 and y = 3 and the pair x = -9 and y = -3.<BR>\n" );
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document.write( "You can validate these two sets of answers by returning to the original equations and<BR>\n" );
document.write( "convincing yourself that by substituting +9 for x and +3 for y will make both equations true<BR>\n" );
document.write( "and then by substituting -9 for x and -3 for y both equations will also still balance.<BR>\n" );
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document.write( "Hope this helps you to see your way through the problem.<BR>\n" );
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