document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190105>Question 190105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve this system using the Addition Method:\r<BR>\n" );
document.write( "\n" );
document.write( "3x - y = -1\r<BR>\n" );
document.write( "\n" );
document.write( "4x + 2y = 22 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142694 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=142694\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we are given the system of equations as:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+y+=+-1+ ALIGN=MIDDLE  ALT=\"+3x+-+y+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > .............. (1)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x+%2B+2y+=+22+ ALIGN=MIDDLE  ALT=\"+4x+%2B+2y+=+22+\"   DISABLED_style= \"max-width:90%; height:auto;\" > .............. (2)\r<BR>\n" );
document.write( "\n" );
document.write( "multiply equation (1) by 2, we get:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A%283x+-+y%29+=+2%2A%28-1%29+ ALIGN=MIDDLE  ALT=\"+2%2A%283x+-+y%29+=+2%2A%28-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (now, use the distributive law to open the brackets)<BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6x+-+2y+=+-2+ ALIGN=MIDDLE  ALT=\"+6x+-+2y+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > .............. (3)\r<BR>\n" );
document.write( "\n" );
document.write( "Now Add equations (3) with equation (2). (In the addition method, we need to make the coefficients of either variable of opposite signs so that on adding the two equations the terms cancel out.)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x+%2B+cross%282y%29+=+22+ ALIGN=MIDDLE  ALT=\"+4x+%2B+cross%282y%29+=+22+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6x+-+cross%282y%29+=+-2+ ALIGN=MIDDLE  ALT=\"+6x+-+cross%282y%29+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "_________________________<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10x++++++++=+20+ ALIGN=MIDDLE  ALT=\"+10x++++++++=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+20%2F10+ ALIGN=MIDDLE  ALT=\"+x+=+20%2F10+\"   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+=+2%29+ ALIGN=MIDDLE  ALT=\"+highlight%28x+=+2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "now plug in this value of x onto any of the equations (1) or (2) and get the value of y,\r<BR>\n" );
document.write( "\n" );
document.write( "from equation (1) we get:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+y+=+-1+ ALIGN=MIDDLE  ALT=\"+3x+-+y+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%282%29+-+y+=+-1+ ALIGN=MIDDLE  ALT=\"+3%282%29+-+y+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+-+y+=+-1+ ALIGN=MIDDLE  ALT=\"+6+-+y+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-+y+=+-1+-+6+ ALIGN=MIDDLE  ALT=\"+-+y+=+-1+-+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-+y+=+-7+ ALIGN=MIDDLE  ALT=\"+-+y+=+-7+\"   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+=+7%29+ ALIGN=MIDDLE  ALT=\"+highlight%28y+=+7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so, we have our x and y values...<BR>\n" );
document.write( "we can check them by plugging these values into the equations (1) and (2).\r<BR>\n" );
document.write( "\n" );
document.write( "from (1) we get:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+y+=+-1+ ALIGN=MIDDLE  ALT=\"+3x+-+y+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%282%29+-+7+=+-1+ ALIGN=MIDDLE  ALT=\"+3%282%29+-+7+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+-+7+=+-1+ ALIGN=MIDDLE  ALT=\"+6+-+7+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1+=+-1+ ALIGN=MIDDLE  ALT=\"+-1+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which is true.\r<BR>\n" );
document.write( "\n" );
document.write( "from (2) we get:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x+%2B+2y+=+22+ ALIGN=MIDDLE  ALT=\"+4x+%2B+2y+=+22+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%282%29+%2B+2%287%29+=+22+ ALIGN=MIDDLE  ALT=\"+4%282%29+%2B+2%287%29+=+22+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8+%2B+14+=+22+ ALIGN=MIDDLE  ALT=\"+8+%2B+14+=+22+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+22+=+22+ ALIGN=MIDDLE  ALT=\"+22+=+22+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is again true.\r<BR>\n" );
document.write( "\n" );
document.write( "so our values of x and y are correct !\r<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );