document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=537186>Question 537186</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I am trying to figure out how to solve a system by the method of substitution. I have two problems in which I am having trouble with.\r<BR>\n" );
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document.write( "1) {x+3y=8 <BR>\n" );
document.write( "   {y= 2x-9\r<BR>\n" );
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document.write( "and \r<BR>\n" );
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document.write( "2) {5x+2y=0<BR>\n" );
document.write( "   {x-3y=0\r<BR>\n" );
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document.write( "I'm confused on how to begin and the proper way to solve the problem, thank you for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #352749 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=352749\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve a system of two linear equations by substitution, you solve for one of the variables in one equation and substitute the expression found in the other.<BR>\n" );
document.write( "Let's see how it works for your problems.<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3y=8 ALIGN=MIDDLE  ALT=\"x%2B3y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+2x-9 ALIGN=MIDDLE  ALT=\"y=+2x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Half of the work is already done for you because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+2x-9 ALIGN=MIDDLE  ALT=\"y=+2x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is already \"solved\" for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so you just substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-9 ALIGN=MIDDLE  ALT=\"2x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the other equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%282x-9%29=8 ALIGN=MIDDLE  ALT=\"x%2B3%282x-9%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply (apply distributive property)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B6x-27=8 ALIGN=MIDDLE  ALT=\"x%2B6x-27=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Collect like terms (distributive property backwards, adding apples to apples and x's to x's)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x-27=8 ALIGN=MIDDLE  ALT=\"7x-27=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add 27 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x=8%2B27 ALIGN=MIDDLE  ALT=\"7x=8%2B27\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x=35 ALIGN=MIDDLE  ALT=\"7x=35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by 7<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then go back to find y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-9=2%2A5-9=1 ALIGN=MIDDLE  ALT=\"y=2x-9=2%2A5-9=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the answer is x=5 with y=1, usually expressed as the pair (5, 1).<BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B2y=0 ALIGN=MIDDLE  ALT=\"5x%2B2y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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;\" ><BR>\n" );
document.write( "You need to solve for x or for y one of the two equations I would go with x in the second one:<BR>\n" );
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;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3y ALIGN=MIDDLE  ALT=\"x=3y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then substitute in the first equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%283y%29%2B2y=0 ALIGN=MIDDLE  ALT=\"5%283y%29%2B2y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15y%2B2y=0 ALIGN=MIDDLE  ALT=\"15y%2B2y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15y=0 ALIGN=MIDDLE  ALT=\"15y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3y=3%2A0=0 ALIGN=MIDDLE  ALT=\"x=3y=3%2A0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solution is (0, 0). </SPAN>\n" );
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