document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=8520>Question 8520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The worksheet says:<BR>\n" );
document.write( "Use substitution to solve each system of equations.  If the system does not have exactly one solution, state whether it has no solution or infinitely many solutions.\r<BR>\n" );
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document.write( "The problem:<BR>\n" );
document.write( "3x-y=4<BR>\n" );
document.write( "2x-3y=-9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4711 by </B><A HREF=/tutors/aboutme.mpl?userid=prince_abubu><B>prince_abubu(198)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=prince_abubu><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=4711\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would play around with the first equation first because it's already got a variable by itself (without a number attached to it by multiplication).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+y+=+4+ ALIGN=MIDDLE  ALT=\"+3x+-+y+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- choose this because one of the variables is already free-standing.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-y+=+4+-+3x+ ALIGN=MIDDLE  ALT=\"+-y+=+4+-+3x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <----- Move the 3x to the right side. (I trust that you know that the sign of the terms change when you move them from one side of the equation to another by addition or subtraction).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-4+%2B+3x+ ALIGN=MIDDLE  ALT=\"+y+=+-4+%2B+3x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- Multiply EVERYTHING by -1 so that the y by itself is positive.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3x+-+4+ ALIGN=MIDDLE  ALT=\"+y+=+3x+-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- Switch the positions of the two terms just because it looks better this way.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+-+3%283x+-+4%29+=+-9+ ALIGN=MIDDLE  ALT=\"+2x+-+3%283x+-+4%29+=+-9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- Take the other equation. Replace the y with the (3x - 4). This is the substitution move.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+-+9x+%2B+12+=+-9+ ALIGN=MIDDLE  ALT=\"+2x+-+9x+%2B+12+=+-9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- Used distributive property\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-7x+%2B+12+=+-9+ ALIGN=MIDDLE  ALT=\"+-7x+%2B+12+=+-9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- Combined like terms by subtraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-7x+=+-21+ ALIGN=MIDDLE  ALT=\"+-7x+=+-21+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- Moved 12 to the right side, combine with the -9 to make the -21.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+3+ ALIGN=MIDDLE  ALT=\"+x+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- Divided by -7 on both sides.\r<BR>\n" );
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document.write( "Now, you've got x = 3. You can go back to ANY two of your original equations and plug in this 3 into the x and solve for y. Notice that we already tweaked the first equation to get it to be in y= form - the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3x+-+4+ ALIGN=MIDDLE  ALT=\"+y+=+3x+-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The y is already solved for. All you have to do is plug in the 3 and you'll get the y:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3%283%29+-+4+=+9+-+4+=+5+ ALIGN=MIDDLE  ALT=\"+y+=+3%283%29+-+4+=+9+-+4+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <----- So x=3 and y=5. </SPAN>\n" );
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