document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190104>Question 190104</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the Substitution Method, solve the system\r<BR>\n" );
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document.write( "2x + 3y = -4\r<BR>\n" );
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document.write( "x - 2y = 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142695 by </B><A HREF=/tutors/aboutme.mpl?userid=cutepiscean5><B>cutepiscean5(19)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=cutepiscean5><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=142695\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we have the given equations as :\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+%2B+3y+=+-4+ ALIGN=MIDDLE  ALT=\"+2x+%2B+3y+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ........ (1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+2y+=+5+ ALIGN=MIDDLE  ALT=\"+x+-+2y+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ............(2)\r<BR>\n" );
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document.write( "from equation (2) we extract x in terms of y and we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+2y+=+5+ ALIGN=MIDDLE  ALT=\"+x+-+2y+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now, add 2y to both sides of the equation, such that 2y on the left hand side cancels out.\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+cross%282y%29+%2B+cross%282y%29+=+2y+%2B+5+ ALIGN=MIDDLE  ALT=\"+x+-+cross%282y%29+%2B+cross%282y%29+=+2y+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+2y+%2B+5+ ALIGN=MIDDLE  ALT=\"+x+=+2y+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ............(3)\r<BR>\n" );
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document.write( "substitute , this value of x into the first equation (1) . we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+%2B+3y+=+-4+ ALIGN=MIDDLE  ALT=\"+2x+%2B+3y+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%282y+%2B+5%29+%2B+3y+=+-4+ ALIGN=MIDDLE  ALT=\"+2%282y+%2B+5%29+%2B+3y+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (use distributive law to open the brackets)<BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4y+%2B+10+%2B+3y+=+-4+ ALIGN=MIDDLE  ALT=\"+4y+%2B+10+%2B+3y+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (now, combine the like terms)<BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7y+%2B+10+=+-4+ ALIGN=MIDDLE  ALT=\"+7y+%2B+10+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Subtract 10 from both sides)<BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7y+=+-4+-+10+ ALIGN=MIDDLE  ALT=\"+7y+=+-4+-+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7y+=+-14+ ALIGN=MIDDLE  ALT=\"+7y+=+-14+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-14%2F7+ ALIGN=MIDDLE  ALT=\"+y+=+-14%2F7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28y+=+-2%29+ ALIGN=MIDDLE  ALT=\"+highlight%28y+=+-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now plug in this value of y, into the equation (3) to get the value of x,\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+2y+%2B+5+ ALIGN=MIDDLE  ALT=\"+x+=+2y+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+2%28-2%29+%2B+5+ ALIGN=MIDDLE  ALT=\"+x+=+2%28-2%29+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-4+%2B+5+ ALIGN=MIDDLE  ALT=\"+x+=+-4+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28x+=+1%29+ ALIGN=MIDDLE  ALT=\"+highlight%28x+=+1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Checking plug in values of x and y in both equations and verify:\r<BR>\n" );
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document.write( "In Equation (1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+%2B+3y+=+-4+ ALIGN=MIDDLE  ALT=\"+2x+%2B+3y+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%281%29+%2B+3%28-2%29+=+-4+ ALIGN=MIDDLE  ALT=\"+2%281%29+%2B+3%28-2%29+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+-+6+=+-4+ ALIGN=MIDDLE  ALT=\"+2+-+6+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4+=+-4+ ALIGN=MIDDLE  ALT=\"+-4+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is true.\r<BR>\n" );
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document.write( "In Equation (2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+2y+=+5+ ALIGN=MIDDLE  ALT=\"+x+-+2y+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%29+-+2%28-2%29+=+5+ ALIGN=MIDDLE  ALT=\"+%281%29+-+2%28-2%29+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+-+%28-4%29+=+5+ ALIGN=MIDDLE  ALT=\"+1+-+%28-4%29+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+%2B+4+=+5+ ALIGN=MIDDLE  ALT=\"+1+%2B+4+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+=+5+ ALIGN=MIDDLE  ALT=\"+5+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is again true,\r<BR>\n" );
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document.write( "Hence our answers are correct !\r<BR>\n" );
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document.write( "Hope this helps.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );