document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=698899>Question 698899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you help me solve substitution problems. if you dont mind help me solve for x ill just solve for y. 1. 3x+y=25 x=y+3 2. 3x-2y=7 x+3y=-5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #431176 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=431176\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > (For those particular systems, it's easier that way).<BR>\n" );
document.write( "Then you can solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Not all systems lend themselves to an easy resolution by substitution.<BR>\n" );
document.write( "Substitution is easiest when you have one equation in the form y=___  or x=___ ,<BR>\n" );
document.write( "with a simple expression to the right of the equal sign.<BR>\n" );
document.write( "If you can transform one equation into that form and end with an easy expression, it would work too.<BR>\n" );
document.write( "That happens when one of the variables does not have a coefficient in front of it,<BR>\n" );
document.write( "like the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3y=-5 ALIGN=MIDDLE  ALT=\"x%2B3y=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The wise student will chose the easiest way to solve a system,<BR>\n" );
document.write( "because complicated ways increase the risk of making dumb mistakes. <BR>\n" );
document.write( " <BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283x%2By=25%2Cx=y%2B3%29 ALIGN=MIDDLE  ALT=\"system%283x%2By=25%2Cx=y%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this case, you already have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%2B3 ALIGN=MIDDLE  ALT=\"x=y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the right form.<BR>\n" );
document.write( "That equations tells you that the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B3 ALIGN=MIDDLE  ALT=\"y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so I just substitute the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B3 ALIGN=MIDDLE  ALT=\"y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the other equation to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28y%2B3%29%2By=25 ALIGN=MIDDLE  ALT=\"3%28y%2B3%29%2By=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > that I can solve 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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28y%2B3%29%2By=25 ALIGN=MIDDLE  ALT=\"3%28y%2B3%29%2By=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%2B9%2By=25 ALIGN=MIDDLE  ALT=\"3y%2B9%2By=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%2B9=25 ALIGN=MIDDLE  ALT=\"4y%2B9=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=25-9 ALIGN=MIDDLE  ALT=\"4y=25-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=16 ALIGN=MIDDLE  ALT=\"4y=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%2F4=16%2F4 ALIGN=MIDDLE  ALT=\"4y%2F4=16%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=4%29 ALIGN=MIDDLE  ALT=\"highlight%28y=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At this point, I would substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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 equation that will make finding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > easier: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%2B3 ALIGN=MIDDLE  ALT=\"x=y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283x-2y=7%2C+x%2B3y=-5%29 ALIGN=MIDDLE  ALT=\"system%283x-2y=7%2C+x%2B3y=-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The easiest way to transform one of those equation so that one variable is isolated on one side of the equal sign is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3y=-5%29%29%29+--%3E+%7B%7B%7Bx=-3y-5 ALIGN=MIDDLE  ALT=\"x%2B3y=-5%29%29%29+--%3E+%7B%7B%7Bx=-3y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That is a wise choice, that gives me a simple expression for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3y-5 ALIGN=MIDDLE  ALT=\"-3y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y=7 ALIGN=MIDDLE  ALT=\"3x-2y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > , I get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28-3y-5%29-2y=7 ALIGN=MIDDLE  ALT=\"3%28-3y-5%29-2y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which I will solve 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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28-3y-5%29-2y=7 ALIGN=MIDDLE  ALT=\"3%28-3y-5%29-2y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9y-15-2y=7 ALIGN=MIDDLE  ALT=\"-9y-15-2y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11y-15=7 ALIGN=MIDDLE  ALT=\"-11y-15=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11y=7%2B15 ALIGN=MIDDLE  ALT=\"-11y=7%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11y=22 ALIGN=MIDDLE  ALT=\"-11y=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11y%2F%28-11%29=22%2F%28-11%29 ALIGN=MIDDLE  ALT=\"-11y%2F%28-11%29=22%2F%28-11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <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;\" > .<BR>\n" );
document.write( "At this point, I would substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   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 equation that will make finding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > easier.<BR>\n" );
document.write( "Maybe I would use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3y-5 ALIGN=MIDDLE  ALT=\"x=-3y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE:<BR>\n" );
document.write( "A different choice could have complicated my work.<BR>\n" );
document.write( "If I decided to solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y=7 ALIGN=MIDDLE  ALT=\"3x-2y=7\"   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;\" >, I would do<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y=7 ALIGN=MIDDLE  ALT=\"3x-2y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y=7-3x ALIGN=MIDDLE  ALT=\"-2y=7-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y%2F2=7%2F%28-2%29-3x%2F%28-2%29 ALIGN=MIDDLE  ALT=\"-2y%2F2=7%2F%28-2%29-3x%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7%2F2%2B%283%2F2%29x ALIGN=MIDDLE  ALT=\"y=-7%2F2%2B%283%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "That expression 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;\" > has fractions, and will make me likely to make a silly mistake.<BR>\n" );
document.write( "It is sad to lose grade points (and time),<BR>\n" );
document.write( "just because of complicated expressions that lead to silly mistakes,<BR>\n" );
document.write( "especially when you really know your algebra.<BR>\n" );
document.write( "Next, I would be substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2F2%2B%283%2F2%29x ALIGN=MIDDLE  ALT=\"-7%2F2%2B%283%2F2%29x\"   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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3y=-5%29%29%29+to+get%0D%0A%7B%7B%7Bx%2B3%28-7%2F2%2B%283%2F2%29x%29=-5%29%29%29+--%3E+%7B%7B%7Bx-21%2F2%2B%289%2F2%29x=-5%29%29%29+--%3E+%7B%7B%7B%281%2B%289%2F2%29%29x-21%2F2=-5%29%29%29+--%3E+%7B%7B%7B%281%2B%289%2F2%29%29x=-5%2B21%2F2%29%29%29+--%3E+%7B%7B%7B%281%2F2%29x=11%2F2%29%29%29+--%3E+%7B%7B%7Bx=1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(In doing the calculations above,<BR>\n" );
document.write( "I made a mistake with the sign of one of those fractions,<BR>\n" );
document.write( "and I only noticed because I had solved the system the easier way before,<BR>\n" );
document.write( "and had found <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "I had to review carefully to see where I had messed up, and to correct it). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );